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 A100405 Number of partitions of n where every part appears more than two times. 10
 1, 0, 0, 1, 1, 1, 2, 1, 2, 3, 3, 3, 7, 5, 6, 11, 10, 10, 17, 15, 20, 26, 25, 29, 44, 41, 47, 63, 67, 72, 99, 97, 114, 143, 148, 168, 216, 216, 248, 306, 328, 358, 443, 462, 527, 629, 665, 739, 898, 936, 1055, 1238, 1330, 1465, 1727, 1837, 2055, 2366, 2543, 2808, 3274 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 1..5000 from Vaclav Kotesovec) FORMULA G.f.: Product_{k>0} (1+x^(3*k)/(1-x^k)). More generally, g.f. for number of partitions of n where every part appears more than m times is Product_{k>0} (1+x^((m+1)*k)/(1-x^k)). a(n) ~ sqrt(Pi^2 + 6*c) * exp(sqrt((2*Pi^2/3 + 4*c)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-3*x)) dx = -0.77271248407593487127235205445116662610863126869049971822566... . - Vaclav Kotesovec, Jan 05 2016 EXAMPLE a(6)=2 because we have [2,2,2] and [1,1,1,1,1,1]. MAPLE G:=product((1+x^(3*k)/(1-x^k)), k=1..30): Gser:=series(G, x=0, 80): seq(coeff(Gser, x, n), n=0..70); # Emeric Deutsch, Aug 06 2005 # second Maple program: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(b(n-i*j, i-1), j=[0, \$3..iquo(n, i)])))     end: a:= n-> b(n\$2): seq(a(n), n=0..70);  # Alois P. Heinz, Aug 20 2019 MATHEMATICA nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(3*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *) CROSSREFS Cf. A007690, A160974-A160990. Cf. A266647, A266648, A266649, A266650. Sequence in context: A161078 A161294 A161269 * A081366 A129636 A242443 Adjacent sequences:  A100402 A100403 A100404 * A100406 A100407 A100408 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Jan 11 2005 EXTENSIONS More terms from Emeric Deutsch, Aug 06 2005 a(0)=1 prepended by Alois P. Heinz, Aug 20 2019 STATUS approved

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Last modified July 30 09:18 EDT 2021. Contains 346359 sequences. (Running on oeis4.)