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A100835 Number of partitions of n with at most 2 odd parts. 2
1, 1, 2, 2, 4, 4, 8, 7, 14, 12, 24, 19, 39, 30, 62, 45, 95, 67, 144, 97, 212, 139, 309, 195, 442, 272, 626, 373, 873, 508, 1209, 684, 1653, 915, 2245, 1212, 3019, 1597, 4035, 2087, 5348, 2714, 7051, 3506, 9229, 4508, 12022, 5763, 15565, 7338, 20063, 9296, 25722 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: (1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4))/Product(1-x^(2*i), i=1..infinity). More generally, g.f. for number of partitions of n with at most k odd parts is (1+Sum(x^i/Product(1-x^(2*j), j=1..i), i=1..k))/Product(1-x^(2*i), i=1..infinity).

EXAMPLE

a(5) = 4 because we have [5], [4,1], [3,2] and [2,2,1] (the partitions [3,1,1], [2,1,1,1] and [1,1,1,1,1] do not qualify).

MAPLE

g:=(1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4))/product(1-x^(2*i), i=1..40): gser:=series(g, x, 60): seq(coeff(gser, x, n), n=0..55); # Emeric Deutsch, Feb 16 2006

MATHEMATICA

nmax = 50; CoefficientList[Series[(1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4)) * Product[1/(1-x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 07 2016 *)

CROSSREFS

Cf. A000070, A008951, A000097, A000098, A000710.

Sequence in context: A191234 A225373 A138219 * A120541 A190172 A059867

Adjacent sequences:  A100832 A100833 A100834 * A100836 A100837 A100838

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jan 13 2005

EXTENSIONS

More terms from Emeric Deutsch, Feb 16 2006

STATUS

approved

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Last modified December 7 05:39 EST 2016. Contains 278841 sequences.