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A045847 Matrix whose (i,j)-th entry is number of representations of j as a sum of i squares of nonnegative integers; read by diagonals.

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%I A045847 #28 Apr 01 2018 05:52:52
%S A045847 1,1,0,1,1,0,1,2,0,0,1,3,1,0,0,1,4,3,0,1,0,1,5,6,1,2,0,0,1,6,10,4,3,2,
%T A045847 0,0,1,7,15,10,5,6,0,0,0,1,8,21,20,10,12,3,0,0,0,1,9,28,35,21,21,12,0,
%U A045847 1,1,0,1,10,36,56,42,36,30,4,3,2,0,0,1,11,45,84,78,63,61,20,6,6,2,0,0
%N A045847 Matrix whose (i,j)-th entry is number of representations of j as a sum of i squares of nonnegative integers; read by diagonals.
%H A045847 Seiichi Manyama, <a href="/A045847/b045847.txt">Ascending antidiagonals n = 0..139, flattened</a>
%H A045847 H. Wilf, <a href="https://arxiv.org/abs/math/9809120">A combinatorial determinant</a>, arXiv:math/9809120 [math.CO], 1998.
%F A045847 i-th row is expansion of (1+x+x^4+x^9+...)^i.
%e A045847 Rows are
%e A045847 1,0,0,..;
%e A045847 1,1,0,0,1,0..;
%e A045847 1,2,1,0,2,2,..;
%e A045847 1,3,3,1,...
%Y A045847 Rows k=0-10 give: A000007, A010052, A000925, A002102, A014110, A038671, A045848, A045849, A045850, A045851, A045852.
%Y A045847 Diagonal gives A287617.
%Y A045847 Antidiagonal sums give A302018.
%K A045847 nonn,tabl,easy
%O A045847 0,8
%A A045847 _N. J. A. Sloane_
%E A045847 More terms from _Erich Friedman_