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 A089958 Number of partitions of n in which every part occurs 2, 3, or 5 times. 2
 1, 0, 1, 1, 1, 1, 3, 1, 3, 4, 4, 4, 8, 5, 9, 11, 11, 12, 20, 15, 23, 27, 28, 31, 45, 38, 52, 61, 64, 71, 96, 87, 112, 129, 136, 151, 194, 184, 227, 259, 275, 304, 376, 368, 441, 499, 531, 586, 704, 705, 826, 927, 989, 1088, 1280, 1302, 1500, 1672, 1787, 1960, 2267 (list; graph; refs; listen; history; text; internal format)
 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 Sequence in context: A029152 A320279 A175290 * A162932 A216036 A008924 Adjacent sequences: A089955 A089956 A089957 * A089959 A089960 A089961 KEYWORD nonn AUTHOR Eric W. Weisstein, Nov 16 2003 STATUS approved

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Last modified August 14 02:14 EDT 2024. Contains 375146 sequences. (Running on oeis4.)