A280863 Expansion of 1/(1 - Sum_{k>=0} x^((2*k+1)^2)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 19, 24, 30, 37, 45, 55, 66, 79, 95, 115, 140, 171, 209, 255, 312, 381, 464, 564, 685, 832, 1011, 1229, 1494, 1818, 2214, 2697, 3285, 4000, 4869, 5926, 7211, 8772, 10670, 12980, 15793, 19219, 23391, 28470, 34653, 42179, 51336, 62475, 76025, 92510

Offset

0,10

Comments

Number of compositions (ordered partitions) of n into odd squares (A016754).

Links

Table of n, a(n) for n=0..63.

Index entries for sequences related to sums of squares

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=0} x^((2*k+1)^2)).

Example

a(12) = 5 because we have [9, 1, 1, 1], [1, 9, 1, 1], [1, 1, 9, 1], [1, 1, 1, 9] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

nmax = 63; CoefficientList[Series[1/(1 - Sum[x^(2 k + 1)^2, {k, 0, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000290, A006456, A016754, A167661, A167700, A280542.

Sequence in context: A017903 A005711 A322856 * A059765 A180479 A193456

Adjacent sequences: A280860 A280861 A280862 * A280864 A280865 A280866

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 09 2017

Status

approved