OFFSET
0,7
COMMENTS
Also number of partitions of n in which every part is congruent to {2, 3, 6, 9, 10} mod 12. - Vladeta Jovovic, Jan 07 2005
REFERENCES
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (2.5.5).
M. V. Subbarao, Combinatorial proofs of some identities, Proc. Washington State Univ. Conf. Number Theory, 1971, pp. 80-91.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
M. V. Subbarao, On a partition theorem of MacMahon-Andrews, Proc. Amer. Math. Soc., 27, 1971, 449-450.
Eric Weisstein's World of Mathematics, Partition Function P
FORMULA
Euler transform of period 12 sequence [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, ...]. - Vladeta Jovovic, Jan 07 2005
Expansion of q^(-5/24)eta(q^6)eta(q^4)/(eta(q^2)eta(q^3)) in powers of q.
G.f.: Product_{j>=1}(1+x^(2j)+x^(3j)+x^(5j)). - Emeric Deutsch, Mar 05 2006
a(n) ~ 5^(1/4) * exp(Pi*sqrt(5*n/2)/3) / (2^(11/4) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Aug 24 2015
EXAMPLE
a(11) = 4 because we have [4,4,1,1,1], [3,3,3,1,1], [3,3,1,1,1,1,1] and [2,2,2,1,1,1,1,1].
MAPLE
g:=product(1+x^(2*j)+x^(3*j)+x^(5*j), j=1..50): gser:=series(g, x=0, 63): seq(coeff(gser, x, n), n=0..60); # Emeric Deutsch, Mar 05 2006
MATHEMATICA
nn = 60; CoefficientList[ Series[Product[1 + x^(2 i) + x^(3 i) + x^(5 i), {i, 1, nn}], {x, 0, nn}], x] (* Geoffrey Critzer, May 31 2013 *)
QP = QPochhammer; s = QP[q^6]*(QP[q^4]/(QP[q^2]*QP[q^3])) + O[q]^70; CoefficientList[s, q] (* Jean-François Alcover, Nov 30 2015, adapted from PARI *)
PROG
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^4+A) *eta(x^6+A)/eta(x^2+A)/eta(x^3+A), n))} /* Michael Somos, Jan 19 2005 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Nov 16 2003
STATUS
approved