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A132463 Number of partitions of n into distinct parts congruent to 0 or 1 modulo 3. 6
1, 1, 0, 1, 2, 1, 1, 3, 2, 2, 5, 4, 3, 7, 7, 5, 10, 11, 8, 14, 17, 13, 20, 25, 19, 27, 36, 29, 37, 50, 43, 51, 69, 61, 69, 94, 86, 93, 126, 120, 125, 167, 164, 167, 220, 222, 222, 287, 297, 294, 373, 393, 386, 481, 516, 505, 617, 672, 657, 788, 868, 850, 1002, 1114, 1094 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Reinhard Zumkeller and Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 201 terms from Reinhard Zumkeller)

FORMULA

G.f.: Product(k>=1, (1+x^(3*k))*(1+x^(3*k-2)) ). - Emeric Deutsch, Aug 26 2007

a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(19/12) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Aug 24 2015

EXAMPLE

a(7)=3 because we have 7, 61 and 43.

MAPLE

g:=product((1+x^(3*k))*(1+x^(3*k-2)), k=1..30): gser:=series(g, x=0, 100): seq(coeff(gser, x, n), n=0..65); # Emeric Deutsch, Aug 26 2007

MATHEMATICA

nmax = 100; CoefficientList[Series[Product[((1+x^(3*k))*(1+x^(3*k-2))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 24 2015 *)

CROSSREFS

Cf. A032766, A035360, A003105, A132462.

Sequence in context: A132462 A161039 A104467 * A153901 A132844 A006843

Adjacent sequences:  A132460 A132461 A132462 * A132464 A132465 A132466

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 22 2007

EXTENSIONS

Prepended a(0) = 1, Joerg Arndt, Feb 22 2015

STATUS

approved

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Last modified September 18 12:28 EDT 2020. Contains 337169 sequences. (Running on oeis4.)