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%I #14 Dec 03 2017 17:17:19
%S 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,
%T 56,56,7,19,34,50,65,77,84,84,8,22,40,60,80,98,112,120,120,9,25,46,70,
%U 95,119,140,156,165,165,10,28,52,80,110,140,168,192,210,220,220,11,31,58
%N Array T(n,k) = binomial(k+2, k-1) + n*binomial(k+2, k) read by antidiagonals.
%H D. A. Sardelis, T. M. Valahas, <a href="http://arxiv.org/abs/0805.4070">On Multidimensional Pythagorean Numbers</a>, arxiv:0805.4070 [math.GM], 2008, Table 6, eq 12.
%F T(n,k) = binomial(k+2, 3) + n*binomial(k+2, 2).
%e The array starts in row n=0 with columns k >= 0 as
%e 0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, ...
%e 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, ...
%e 2, 7, 16, 30, 50, 77, 112, 156, 210, 275, 352, ...
%e 3, 10, 22, 40, 65, 98, 140, 192, 255, 330, 418, ...
%e 4, 13, 28, 50, 80, 119, 168, 228, 300, 385, 484, ...
%e 5, 16, 34, 60, 95, 140, 196, 264, 345, 440, 550, ...
%e ...
%p A140765 := proc(n,k) binomial(k+2,k-1)+n*binomial(k+2,k) ; end proc:
%p # _R. J. Mathar_, Aug 31 2011
%t T[n_, k_] := Binomial[k + 2, k - 1] + n Binomial[k + 2, k];
%t Table[T[n - k, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Dec 03 2017 *)
%K nonn,tabl,easy
%O 0,4
%A _Gary W. Adamson_, May 28 2008
%E Definition substantiated by _R. J. Mathar_, Aug 31 2011
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