A045847 - OEIS

%I #28 Apr 01 2018 05:52:52

%S 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 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 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 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 Seiichi Manyama, <a href="/A045847/b045847.txt">Ascending antidiagonals n = 0..139, flattened</a>

%H H. Wilf, <a href="https://arxiv.org/abs/math/9809120">A combinatorial determinant</a>, arXiv:math/9809120 [math.CO], 1998.

%F i-th row is expansion of (1+x+x^4+x^9+...)^i.

%e Rows are

%e 1,0,0,..;

%e 1,1,0,0,1,0..;

%e 1,2,1,0,2,2,..;

%e 1,3,3,1,...

%Y Rows k=0-10 give: A000007, A010052, A000925, A002102, A014110, A038671, A045848, A045849, A045850, A045851, A045852.

%Y Diagonal gives A287617.

%Y Antidiagonal sums give A302018.

%K nonn,tabl,easy

%O 0,8

%A _N. J. A. Sloane_

%E More terms from _Erich Friedman_