cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

Original entry on oeis.org

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

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Author

Keywords

Examples

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

Crossrefs

Diagonal gives A287617.
Antidiagonal sums give A302018.

Formula

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

Extensions

More terms from Erich Friedman

A302019 Expansion of 1/(1 - x*Sum_{k>=0} x^(k^3)).

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 21, 34, 56, 91, 149, 243, 397, 648, 1058, 1727, 2819, 4602, 7512, 12263, 20018, 32678, 53344, 87080, 142151, 232050, 378803, 618366, 1009433, 1647819, 2689933, 4391101, 7168122, 11701387, 19101580, 31181804, 50901806, 83093134, 135642908, 221426218, 361460624
Offset: 0

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Author

Ilya Gutkovskiy, Mar 30 2018

Keywords

Crossrefs

Antidiagonal sums of A290054.

Programs

  • Mathematica
    nmax = 41; CoefficientList[Series[1/(1 - x Sum[x^k^3, {k, 0, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - x*Sum_{k>=0} x^(k^3)).
a(0) = 1; a(n) = Sum_{k=1..n} A010057(k-1)*a(n-k).
Showing 1-2 of 2 results.