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A035592 Number of partitions of 3n with same number of parts == 1 (mod 3) and == 2 (mod 3). 4
1, 2, 6, 14, 32, 66, 134, 256, 480, 868, 1540, 2664, 4536, 7574, 12474, 20234, 32428, 51324, 80388, 124582, 191310, 291114, 439394, 657936, 978054, 1443684, 2117136, 3085174, 4469368, 6437742, 9223324, 13145792, 18644484, 26317916, 36981828 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = A035536(3*n).

G.f.: (Sum_{k>=0} (-1)^k * x^(k * (k + 1)/2)) / (Product_{k>0} 1 - x^k)^3. - Michael Somos, Jul 28 2003

PROG

(PARI) {a(n) = if( n<0, 0, polcoeff( sum( k=0, (sqrtint(1 + 8*n) - 1)\2, (-1)^k * x^((k+k^2)/2)) / eta(x + x * O(x^n))^3, n))} /* Michael Somos, Jul 28 2003 */

CROSSREFS

Cf. A035536.

Sequence in context: A188493 A055292 A327049 * A327050 A301554 A217941

Adjacent sequences: A035589 A035590 A035591 * A035593 A035594 A035595

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

More terms from David W. Wilson

STATUS

approved

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Last modified December 9 11:20 EST 2022. Contains 358700 sequences. (Running on oeis4.)