type CreateArray<T extends number, K extends any[] = []> = K['length'] extends T
  ? K
  : CreateArray<T, [any, ...K]>

type CreateTriangular<N extends number> = [
  ...CreateArray<N>,
  ...(CreateArray<N> extends [any, ...infer R]
    ? CreateTriangular<R['length']>
    : [])
]
type Triangular<N extends number> = CreateTriangular<N>['length']

Solution by Keith-Web3 #34848

type Triangular<N extends number, U extends 0[] = [], R extends 0[] = []> = U['length'] extends N ? R['length'] : Triangular<N, [...U, 0], [...R, ...U, 0]>

Solution by ouzexi #34153

type Triangular<
  N extends number,
  Current extends 0[] = [],
  Prev extends 0[] = [],
> =
  Current['length'] extends N
    ? Prev['length']
    : Triangular<N, [...Current, 0], [...Current, ...Prev, 0]>

Solution by drylint #34135

type Triangular<
  N extends number,
  Temp extends any[] = [],
  Ret extends any[] = []
> = N extends Temp["length"]
  ? Ret["length"]
  : Triangular<N, [...Temp, any], [...Ret, ...Temp, any]>;

Solution by sunupupup #33485

type Triangular<N extends number, Count extends 1[] = [], Result extends 1[] = []>
  = Count['length'] extends N ? Result['length']
  : Triangular<N, [...Count, 1], [...Result, ...Count, 1]>

Playground

Solution by teamchong #33002

type GenerateArray<N extends number, Acc extends number[] = []> = Acc['length'] extends N
  ? Acc
  : GenerateArray<N, [...Acc, Acc['length']]>

type Flatten<T extends unknown[], A extends unknown[] = []> = T extends [] ? A : (T extends [infer F, ...infer R] ? (F extends unknown[] ? Flatten<[...F, ...R], A> :  Flatten<R, [...A, F]>): never);

type Triangular<N extends number, Acc extends unknown[] = []> = Acc['length'] extends N
  ? Flatten<[Acc, GenerateArray<Acc['length']>]>['length']
  : Triangular<N, [...Acc, GenerateArray<Acc['length']>]>

Solution by keyurparalkar #32819

type Triangular<
  N extends number,
  Count extends any[] = [],
  Total extends any[] = []
> = Equal<number, N> extends true
  ? never
  : N extends Count["length"]
  ? Total["length"]
  : Triangular<N, [...Count, ""], [...Total, ...Count, ""]>;

Solution by Vampirelee #32578

type Triangular<
  N extends number,
  T extends any[] = [],
  U extends any[] = []
> = T["length"] extends N
  ? U["length"]
  : Triangular<N, [...T, any], [...U, ...T, any]>;

Solution by moonpoet #31045

type Triangular<
  N extends number,
  U extends unknown[] = [],
  R extends unknown[] = []
> = U['length'] extends N
      ? R['length']
      : Triangular<N, [...U, unknown], [...R, ...U, unknown]>

Solution by milletlovemouse #30990

type Triangular<N extends number, U extends any[] = [], O extends any[] = []> = U['length'] extends N ? [...O, ...U]['length'] : Triangular<N, [...U, 1], [...O, ...U]>

Solution by dreamluo-plus #30699

type Triangular<
  N extends number,
  Count extends number[] = [],
  Res extends number[] = []
> = Count["length"] extends N
  ? [...Res, ...Count]["length"]
  : Triangular<N, [...Count, 1], [...Res, ...Count]>;

Solution by DoubleWoodLin #28918

type BuildArry<Length extends number, Arr extends unknown[] = []> = Arr['length'] extends Length ? Arr : BuildArry<Length, [...Arr, unknown]>
type sub<n1 extends number, n2 extends number> = BuildArry extends [...arr1: BuildArry, ...arr2: infer rest] ? rest['length'] : never;

type Triangular<N extends number, Arr extends unknown[] = []> = N extends 0 ? Arr['length'] : Triangular<sub<N, 1>, [...Arr, ...BuildArry]>

Solution by kekekgwj #28858

type CartesianProduct<T, U> = T extends T ? U extends U ? [T, U] : never : never

Solution by kekekgwj #28855

计算的题目基本上都用数组来实现，利用数组的 length 求和，这题相当于需要把每个数转成对应长度的数组，例如 3，需要转成 1，2，3 这三个数字对应长度的数组

1: ['']
2: ['', ''],
3: ['', '', ''],

递归创建即可

type CountArr<N extends number, R extends string[] = []> = R['length'] extends N 
  ? R
  : CountArr<N, [...R, '']>

type Triangular<N extends number, R extends any[] = [], Count extends string[] = []> = Count['length'] extends N 
  ? R['length']
  : Triangular<N, [...CountArr<[...Count, ""]['length']>, ...R], [...Count, ""]>

Solution by linjunc #28553

type Triangular<N extends number, _Carriage extends 1[][] = [], _Passenger extends 1[] = [], _Next extends 1[] = _Carriage extends [...any, infer L extends 1[]] ? [...L, 1] : [1]> = _Carriage[`length`] extends N ?
  _Passenger[`length`] :
  Triangular<N, [..._Carriage, _Next], [..._Passenger, ..._Next]>;

Solution by E-uler #28099

The method is derived from Sobes76rus's solution

type Reverse<S extends string> = S extends `${infer F}${infer R}`
  ? `${Reverse<R>}${F}`
  : S;

type NextDigit = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0];

type AddOne<S extends string> = S extends `${infer F extends number}${infer R}`
  ? F extends 9
    ? `0${AddOne<R>}`
    : `${NextDigit[F]}${R}`
  : `1`;

type AddN<
  N extends number,
  Sum extends string,
  I extends 1[] = []
> = I['length'] extends N ? Sum : AddN<N, AddOne<Sum>, [...I, 1]>;

type Triangular<
  N extends number,
  I extends 1[] = [],
  R extends string = '0'
> = I['length'] extends N
  ? Reverse<R> extends `${infer RN extends number}`
    ? RN
    : never
  : Triangular<N, [...I, 1], AddN<[...I, 1]['length'] & number, R>>;

Solution by JohnLi1999 #28019