A140765 Array T(n,k) = binomial(k+2, k-1) + n*binomial(k+2, k) read by antidiagonals.

0, 1, 1, 2, 4, 4, 3, 7, 10, 10, 4, 10, 16, 20, 20, 5, 13, 22, 30, 35, 35, 6, 16, 28, 40, 50, 56, 56, 7, 19, 34, 50, 65, 77, 84, 84, 8, 22, 40, 60, 80, 98, 112, 120, 120, 9, 25, 46, 70, 95, 119, 140, 156, 165, 165, 10, 28, 52, 80, 110, 140, 168, 192, 210, 220, 220, 11, 31, 58

Offset

0,4

Links

Table of n, a(n) for n=0..68.

D. A. Sardelis, T. M. Valahas, On Multidimensional Pythagorean Numbers, arxiv:0805.4070 [math.GM], 2008, Table 6, eq 12.

Formula

T(n,k) = binomial(k+2, 3) + n*binomial(k+2, 2).

Example

The array starts in row n=0 with columns k >= 0 as
  0,  1,  4, 10, 20,  35,  56,  84, 120, 165, 220, ...
  1,  4, 10, 20, 35,  56,  84, 120, 165, 220, 286, ...
  2,  7, 16, 30, 50,  77, 112, 156, 210, 275, 352, ...
  3, 10, 22, 40, 65,  98, 140, 192, 255, 330, 418, ...
  4, 13, 28, 50, 80, 119, 168, 228, 300, 385, 484, ...
  5, 16, 34, 60, 95, 140, 196, 264, 345, 440, 550, ...
  ...

Maple

A140765 := proc(n, k) binomial(k+2, k-1)+n*binomial(k+2, k) ; end proc:
# R. J. Mathar, Aug 31 2011

Mathematica

T[n_, k_] := Binomial[k + 2, k - 1] + n Binomial[k + 2, k];
Table[T[n - k, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 03 2017 *)

Crossrefs

Sequence in context: A098217 A151846 A131118 * A097541 A151819 A079560

Adjacent sequences: A140762 A140763 A140764 * A140766 A140767 A140768

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, May 28 2008

Extensions

Definition substantiated by R. J. Mathar, Aug 31 2011

Status

approved