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A140765 Array T(n,k) = binomial(k+2, k-1) + n*binomial(k+2, k) read by antidiagonals. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 08:44 EST 2021. Contains 349426 sequences. (Running on oeis4.)