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A132462 Number of partitions of n into distinct parts congruent to 0 or 2 modulo 3. 7
1, 0, 1, 1, 0, 2, 1, 1, 3, 2, 2, 5, 2, 4, 7, 4, 7, 10, 6, 11, 14, 9, 17, 19, 14, 25, 26, 21, 36, 35, 31, 50, 47, 45, 69, 63, 64, 93, 84, 89, 125, 111, 124, 165, 147, 169, 216, 194, 227, 281, 254, 303, 363, 332, 400, 466, 432, 523, 595, 559, 680, 756, 721, 876, 956, 926, 1121 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
LINKS
FORMULA
G.f.: Product_{k>=1} ((1+x^(3*k))*(1+x^(3*k-1)). - Emeric Deutsch, Aug 30 2007
a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(23/12) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Aug 24 2015
EXAMPLE
a(8)=3 because we have 8, 6+2 and 5+3.
MAPLE
g:=product((1+x^(3*k))*(1+x^(3*k-1)), k=1..30): gser:=series(g, x=0, 100): seq(coeff(gser, x, n), n=0..70); # Emeric Deutsch, Aug 30 2007
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[((1+x^(3*k))*(1+x^(3*k-1))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 24 2015 *)
CROSSREFS
Sequence in context: A228668 A058636 A226009 * A161039 A104467 A132463
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 22 2007
EXTENSIONS
a(0)=1 prepended by Vaclav Kotesovec, Aug 24 2015
STATUS
approved

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Last modified July 20 22:01 EDT 2024. Contains 374459 sequences. (Running on oeis4.)