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.

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, 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, 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

Offset

0,8

Links

Seiichi Manyama, Ascending antidiagonals n = 0..139, flattened

H. Wilf, A combinatorial determinant, arXiv:math/9809120 [math.CO], 1998.

Formula

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

Example

Rows are
1,0,0,..;
1,1,0,0,1,0..;
1,2,1,0,2,2,..;
1,3,3,1,...

Crossrefs

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

Diagonal gives A287617.

Antidiagonal sums give A302018.

Sequence in context: A290054 A290430 A290429 * A137586 A291170 A275001

Adjacent sequences: A045844 A045845 A045846 * A045848 A045849 A045850

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane

Extensions

More terms from Erich Friedman

Status

approved