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 A103265 Number of partitions of n in which both even and odd square parts occur in 2 forms c, c* and with multiplicity 1. There no restriction on parts which are twice squares. 12
 1, 2, 2, 2, 4, 6, 6, 6, 8, 12, 14, 14, 16, 22, 26, 26, 30, 38, 44, 46, 52, 62, 70, 74, 80, 96, 110, 116, 124, 146, 166, 174, 186, 210, 238, 254, 272, 302, 338, 362, 384, 426, 470, 502, 532, 588, 646, 686, 726, 792, 872, 926, 980, 1062 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Convolution of A001156 and A033461. - Vaclav Kotesovec, Aug 18 2015 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 FORMULA G.f.: product_{k>0}((1+x^k^2)/(1-x^k^2)). a(n) ~ exp(3 * ((4-sqrt(2))*Zeta(3/2))^(2/3) * Pi^(1/3) * n^(1/3) / 4) * ((4-sqrt(2))*Zeta(3/2))^(2/3) / (2^(7/2) * sqrt(3) * Pi^(7/6) * n^(7/6)). - Vaclav Kotesovec, Dec 29 2016 EXAMPLE E.g. a(8)=8 because 8 can be written as 8, 44*, 422, 4*22, 4211*, 4*211*, 2222, 22211*. MAPLE series(product((1+x^(k^2))/(1-x^(k^2)), k=1..100), x=0, 100); MATHEMATICA nmax = 50; CoefficientList[Series[Product[(1+x^(k^2)) / (1-x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *) CROSSREFS Cf. A001156, A015128, A033461, A280263, A279227, A306147. Sequence in context: A236840 A182539 A170887 * A341695 A008238 A218870 Adjacent sequences:  A103262 A103263 A103264 * A103266 A103267 A103268 KEYWORD easy,nonn AUTHOR Noureddine Chair, Feb 27 2005 STATUS approved

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Last modified April 15 18:51 EDT 2021. Contains 342977 sequences. (Running on oeis4.)