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 A092295 Number of partitions of n with even number (or 0) 2's. 5
 1, 1, 1, 2, 4, 5, 7, 10, 15, 20, 27, 36, 50, 65, 85, 111, 146, 186, 239, 304, 388, 488, 614, 767, 961, 1191, 1475, 1819, 2243, 2746, 3361, 4096, 4988, 6047, 7322, 8836, 10655, 12801, 15360, 18384, 21978, 26199, 31196, 37062, 43979, 52072, 61579, 72682 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 FORMULA a(n) = A000041(n)-a(n-2). G.f.=1/[(1+x^2)*product(1-x^j, j=1..infinity)]. - Emeric Deutsch, Mar 30 2006 a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*n*sqrt(3)). - Vaclav Kotesovec, Oct 30 2015 EXAMPLE a(5)=5 because the partitions [5],[4,1],[3,1,1],[2,2,1] and [1,1,1,1,1] of 5 have an even number of 2's ([3,2] and [2,1,1,1] do not qualify). MAPLE g:=1/(1+x^2)/product(1-x^j, j=1..70): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=0..47); # Emeric Deutsch, Mar 30 2006 MATHEMATICA nmax = 50; CoefficientList[Series[1/((1+x^2) * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 30 2015 *) CROSSREFS Cf. A087787. Sequence in context: A351390 A218074 A241735 * A277102 A168639 A275802 Adjacent sequences: A092292 A092293 A092294 * A092296 A092297 A092298 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Feb 06 2004 EXTENSIONS More terms from Benoit Cloitre, Feb 08 2004 STATUS approved

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Last modified August 13 20:02 EDT 2024. Contains 375144 sequences. (Running on oeis4.)