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 A096778 Number of partitions of n with at most two even parts. 3
 1, 1, 2, 3, 5, 7, 10, 14, 19, 26, 34, 45, 58, 75, 95, 121, 151, 189, 234, 289, 354, 433, 526, 637, 768, 923, 1105, 1319, 1569, 1861, 2202, 2597, 3056, 3587, 4201, 4908, 5723, 6658, 7732, 8961, 10367, 11971, 13802, 15884, 18253, 20942, 23992, 27445, 31353 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also number of partitions of n+4 with exactly two even parts. Example: a(3)=3 because the partitions of 7 with exactly two even parts are [4,2,1], [3,2,2] and [2,2,1,1,1]. a(n)=A116482(n+4,2). - Emeric Deutsch, Feb 21 2006 REFERENCES Fulman, Jason. Random matrix theory over finite fields. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 51--85. MR1864086 (2002i:60012). See top of page 70, Eq. 2, with k=2. - N. J. A. Sloane, Aug 31 2014 LINKS FORMULA G.f.: (1/((1-x^2)*(1-x^4)))/Product(1-x^(2*i+1), i=0..infinity). More generally, g.f. for number of partitions of n with at most k even parts is (1/Product(1-x^(2*i), i=1..k))/Product(1-x^(2*i+1), i=0..infinity). a(n) ~ 3^(3/4) * n^(1/4) * exp(Pi*sqrt(n/3)) / (8*Pi^2). - Vaclav Kotesovec, May 29 2018 EXAMPLE a(3)=3 because we have ,[2,1] and [1,1,1]. MATHEMATICA CoefficientList[ Series[(1/((1 - x^2)*(1 - x^4)))/Product[1 - x^(2i + 1), {i, 0, 50}], {x, 0, 48}], x] (* Robert G. Wilson v, Aug 16 2004 *) CROSSREFS Cf. A038348. Cf. A116482. Sequence in context: A238658 A116480 A023026 * A325862 A280277 A102108 Adjacent sequences:  A096775 A096776 A096777 * A096779 A096780 A096781 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Aug 16 2004 EXTENSIONS More terms from Robert G. Wilson v, Aug 17 2004 More terms from Emeric Deutsch, Feb 21 2006 STATUS approved

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Last modified January 20 21:46 EST 2022. Contains 350472 sequences. (Running on oeis4.)