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A280129 Expansion of Product_{k>=2} (1 + x^(k^2)). 6
1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 3, 0, 0, 1, 1, 1, 0, 0, 1, 3, 0, 0, 2, 2, 0, 1, 2, 0, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,26

COMMENTS

Number of partitions of n into distinct squares > 1.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=2} (1 + x^(k^2)).

From Vaclav Kotesovec, Dec 26 2016: (Start)

a(n) = Sum_{k=0..n} (-1)^(n-k) * A033461(k).

a(n) + a(n-1) = A033461(n).

a(n) ~ A033461(n)/2.

(End)

EXAMPLE

G.f. = 1 + x^4 + x^9 + x^13 + x^16 + x^20 + 2*x^25 + 2*x^29 + x^34 + x^36 + ...

a(25) = 2 because we have [25] and [16, 9].

MATHEMATICA

nmax = 115; CoefficientList[Series[Product[1 + x^k^2, {k, 2, nmax}], {x, 0, nmax}], x]

PROG

(PARI) {a(n) = if(n < 0, 0, polcoeff( prod(k=2, sqrtint(n), 1 + x^k^2 + x*O(x^n)), n))}; /* Michael Somos, Dec 26 2016 */

CROSSREFS

Cf. A001156, A033461, A078134.

Sequence in context: A226369 A263764 A070202 * A227344 A130207 A167688

Adjacent sequences:  A280126 A280127 A280128 * A280130 A280131 A280132

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 26 2016

STATUS

approved

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Last modified September 25 01:17 EDT 2018. Contains 315360 sequences. (Running on oeis4.)