A280542 Expansion of 1/(1 - Sum_{k>=2} x^(k^2)).

1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 3, 4, 3, 0, 4, 8, 6, 1, 5, 14, 10, 4, 7, 22, 20, 10, 12, 32, 39, 20, 21, 49, 70, 42, 37, 79, 116, 88, 65, 129, 193, 174, 122, 207, 326, 320, 238, 333, 551, 575, 463, 555, 914, 1029, 874, 959, 1502, 1829, 1621, 1691, 2486, 3192, 2989, 3000, 4172, 5488

Offset

0,14

Comments

Number of compositions (ordered partitions) of n into squares > 1.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=2} x^(k^2)).

Example

a(17) = 3 because we have [9, 4, 4], [4, 9, 4] and [4, 4, 9].

Mathematica

nmax = 75; CoefficientList[Series[1/(1 - Sum[x^k^2, {k, 2, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000290, A006456, A078134.

Sequence in context: A340829 A352551 A174739 * A340378 A274575 A203994

Adjacent sequences: A280539 A280540 A280541 * A280543 A280544 A280545

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 05 2017

Status

approved