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A117956 Number of partitions of n into exactly 2 types of parts: one odd and one even. 4
0, 0, 1, 1, 4, 3, 8, 6, 13, 10, 19, 13, 26, 20, 32, 23, 41, 31, 49, 34, 58, 45, 66, 47, 76, 60, 88, 60, 96, 76, 106, 76, 122, 93, 126, 94, 140, 111, 158, 106, 163, 134, 175, 127, 196, 150, 198, 149, 212, 170, 240, 164, 238, 200, 250, 180, 284, 214, 277, 216, 292, 238 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

REFERENCES

N. BENYAHIA TANI, S. BOUROUBI, O. KIHEL, An effective approach for integer partitions using exactly two distinct sizes of parts, Bulletin du Laboratoire, 03 (2015) 18 - 27; Availaible on line at http://www.liforce.usthb.dz.

D Christopher, T Nadu, Partitions with Fixed Number of Sizes, Journal of Integer Sequences, 15 (2015), #15.11.5.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

N. Benyahia Tani, Sadek Bouroubi, Enumeration of the Partitions of an Integer into Parts of a Specified Number of Different Sizes and Especially Two Sizes, J. Int. Seq. 14 (2011) # 11.3.6

FORMULA

G.f.=sum(sum(x^(2i+2j-2)/[(1-x^(2i-1))(1-x^(2j-1))], j=1..i-1), i=1..infinity).

Convolution of x(n) and y(n), where x(n) is the number of even divisors of n and y(n) is the number of odd divisors of n. - Vladeta Jovovic, Apr 05 2006

EXAMPLE

a(7)=8 because we have [6,1],[5,2],[4,3],[4,1,1,1],[3,2,2],[2,2,2,1],[2,2,1,1,1] and [2,1,1,1,1,1].

MAPLE

g:=sum(sum(x^(2*i+2*j-1)/(1-x^(2*i-1))/(1-x^(2*j)), j=1..40), i=1..40): gser:=series(g, x=0, 70): seq(coeff(gser, x^n), n=1..67);

CROSSREFS

Cf. A002133, A117955.

Sequence in context: A189042 A011451 A200089 * A241638 A110662 A265289

Adjacent sequences:  A117953 A117954 A117955 * A117957 A117958 A117959

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Apr 05 2006

STATUS

approved

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Last modified February 23 17:10 EST 2018. Contains 299584 sequences. (Running on oeis4.)