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A103198 Number of compositions of n into a square number of parts. 3
1, 1, 1, 2, 5, 11, 21, 36, 58, 94, 166, 331, 716, 1574, 3368, 6892, 13447, 25127, 45391, 80428, 142615, 259085, 491855, 982400, 2045001, 4352661, 9291361, 19609786, 40574017, 81973315, 161568281, 311062991, 586764281, 1089615033, 2005257849 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..1000

Vaclav Kotesovec, a(n+1)/a(n) as a graph

FORMULA

a(n) = Sum_{k>0} (x/(1-x))^(k^2).

Binomial transform of the characteristic function of squares A010052, with 0th term omitted. - Carl Najafi, Sep 09 2011

MATHEMATICA

nmax = 40; Rest[CoefficientList[Series[-1/2 + EllipticTheta[3, 0, x/(1-x)]/2, {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jan 03 2017 *)

CROSSREFS

Cf. A089333, A052467.

Sequence in context: A113032 A100134 A137356 * A183929 A003522 A112805

Adjacent sequences:  A103195 A103196 A103197 * A103199 A103200 A103201

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Mar 18 2005

STATUS

approved

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Last modified February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)