

A117955


Number of partitions of n into exactly 2 types of odd parts.


5



0, 0, 0, 1, 1, 2, 3, 5, 4, 7, 8, 10, 11, 13, 12, 19, 18, 20, 22, 25, 24, 30, 31, 36, 33, 39, 38, 45, 45, 48, 51, 57, 54, 60, 56, 69, 67, 72, 72, 79, 78, 84, 84, 90, 87, 97, 97, 112, 99, 107, 112, 117, 115, 126, 118, 131, 134, 137, 136, 152, 143, 149, 149, 163, 152, 174, 164
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OFFSET

1,6


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+2j2)/[(1x^(2i1))(1x^(2j1))], j=1..i1), i=1..infinity).
G.f. for number of partitions of n into exactly m types of odd parts is obtained if we substitute x(i) with Sum_{k>0}(x^(2*n1)/(x^(2*n1)1))^i in the cycle index Z(S(m); x(1),x(2),..,x(m)) of the symmetric group S(m) of degree m.  Vladeta Jovovic, Sep 20 2007


EXAMPLE

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


MAPLE

g:=sum(sum(x^(2*i+2*j2)/(1x^(2*i1))/(1x^(2*j1)), j=1..i1), i=1..40): gser:=series(g, x=0, 75): seq(coeff(gser, x^n), n=1..72);


CROSSREFS

Cf. A002133.
Sequence in context: A127515 A256996 A099424 * A074049 A193973 A245057
Adjacent sequences: A117952 A117953 A117954 * A117956 A117957 A117958


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Apr 05 2006


STATUS

approved



