A339279 - OEIS

A339279

Number of partitions of 3*n into powers of 3 where every part appears at least 2 times.

1, 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 18, 22, 25, 29, 34, 38, 43, 50, 55, 62, 70, 77, 85, 95, 103, 113, 126, 136, 149, 164, 177, 192, 210, 225, 243, 265, 283, 305, 330, 352, 377, 406, 431, 460, 494, 523, 557, 595, 629, 667, 710, 748, 791, 841, 884, 934, 989, 1039, 1094, 1156

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..60.

Index entries for sequences related to partitions

FORMULA

G.f.: (1/(1 - x^2)) * Product_{k>=0} 1/(1 - x^(3^k)).

G.f.: (1/(1 - x)) * Product_{k>=0} (1 + x^(2*3^k)/(1 - x^(3^k))).

a(n) = [x^(3*n)] Product_{k>=0} (1 + x^(2*3^k)/(1 - x^(3^k))).

a(n) = Sum_{k=0..n} (-1)^(n-k) * A005704(k).

EXAMPLE

a(3) = 3 because we have [3, 3, 3], [3, 3, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1].

MATHEMATICA

nmax = 60; CoefficientList[Series[(1/(1 - x^2)) Product[1/(1 - x^(3^k)), {k, 0, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x]

A005704[0] = 1; A005704[n_] := A005704[n] = A005704[n - 1] + A005704[Floor[n/3]]; a[n_] := Sum[(-1)^(n - k) A005704[k], {k, 0, n}]; Table[a[n], {n, 0, 60}]

CROSSREFS

Cf. A000244, A005704, A007690, A062051, A339277.

Sequence in context: A332728 A008752 A029003 * A034296 A075745 A214036

Adjacent sequences: A339276 A339277 A339278 * A339280 A339281 A339282

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 29 2020

STATUS

approved