A141675 Triangle, T(n, k) = n*(n-k+1)/(k+1) if n mod k+1 = 0, otherwise T(n, k) = n-k+1, read by rows.

1, 2, 1, 3, 2, 1, 8, 3, 2, 1, 5, 4, 3, 2, 1, 18, 10, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 32, 7, 12, 5, 4, 3, 2, 1, 9, 24, 7, 6, 5, 4, 3, 2, 1, 50, 9, 8, 14, 6, 5, 4, 3, 2, 1

Offset

1,2

Links

G. C. Greubel, Rows n=1..100 of triangle, flattened

Formula

T(n, k) = n*(n-k+1)/(k+1) if n mod k+1 = 0, otherwise T(n, k) = n-k+1.

Example

Triangle begins as:
   1;
   2,  1;
   3,  2,  1;
   8,  3,  2,  1;
   5,  4,  3,  2,  1;
  18, 10,  4,  3,  2,  1;
   7,  6,  5,  4,  3,  2,  1;
  32,  7, 12,  5,  4,  3,  2,  1;
   9, 24,  7,  6,  5,  4,  3,  2,  1;
  50,  9,  8, 14,  6,  5,  4,  3,  2,  1;

Mathematica

T[n_, k_]:= (n-k+1)*If[Mod[n, k+1]==0, n/(k+1), 1];
Table[T[n, k], {n, 12}, {k, n}]//Flatten

Prog

(Magma)
A141675:= func< n, k | (n mod (k+1)) eq 0 select n*(n-k+1)/(k+1) else n-k+1 >;
[A141675(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 06 2024
(SageMath)
def A141675(n, k): return n*(n-k+1)/(k+1) if n%(k+1)==0 else n-k+1
flatten([[A141675(n, k) for k in range(1, n+1)] for n in range(1, 13)]) # G. C. Greubel, Apr 06 2024

Crossrefs

Cf. A126988.

Sequence in context: A162387 A107880 A102228 * A248809 A021473 A266756

Adjacent sequences: A141672 A141673 A141674 * A141676 A141677 A141678

Keyword

nonn

Author

Roger L. Bagula and Gary W. Adamson, Sep 06 2008

Extensions

Edited by G. C. Greubel, Apr 06 2024

Status

approved