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A130780 Number of partitions of n such that number of odd parts is greater than or equal to number of even parts. 12
1, 1, 1, 3, 3, 6, 8, 12, 16, 23, 32, 42, 58, 75, 102, 131, 173, 220, 288, 363, 466, 587, 743, 929, 1164, 1448, 1797, 2224, 2738, 3368, 4122, 5042, 6133, 7466, 9035, 10941, 13184, 15888, 19064, 22876, 27343 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) = A108950(n) + A045931(n) = A000041(n) - A108949(n). - Reinhard Zumkeller, Jan 21 2010

a(n) = Sum_{k=0..n} A240009(n,k). - Alois P. Heinz, Mar 30 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

G.f.: Sum_{k>=0} x^k/Product_{i=1..k} (1-x^(2*i))^2.

EXAMPLE

a(5)=6 because we have 5,41,32,311,211 and 11111 (221 does not qualify).

MAPLE

g:=sum(x^k/(product((1-x^(2*i))^2, i=1..k)), k=0..50): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=1..40); - Emeric Deutsch, Aug 24 2007

# second Maple program:

b:= proc(n, i, t) option remember; `if`(n=0,

      `if`(t>=0, 1, 0), `if`(i<1, 0, b(n, i-1, t)+

      `if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1)))))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..80);  # Alois P. Heinz, Mar 30 2014

MATHEMATICA

$RecursionLimit = 1000; b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t >= 0, 1, 0],  If[i<1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t + (2*Mod[i, 2]-1)]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 80}] (* Jean-Fran├žois Alcover, May 12 2015, after Alois P. Heinz  *)

CROSSREFS

Cf. A045931, A108949, A108950.

Cf. A171966, A171967. - Reinhard Zumkeller, Jan 21 2010

Sequence in context: A241390 A241831 A239946 * A174524 A143592 A280197

Adjacent sequences:  A130777 A130778 A130779 * A130781 A130782 A130783

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 19 2007

EXTENSIONS

More terms from Emeric Deutsch, Aug 24 2007

STATUS

approved

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Last modified December 18 14:30 EST 2018. Contains 318229 sequences. (Running on oeis4.)