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A090723 a(1) = 1; for n > 1, number of partitions of n into distinct odd parts such that the two largest parts differ by 2. 1
1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 2, 1, 1, 3, 3, 1, 2, 4, 3, 2, 3, 5, 5, 3, 4, 7, 6, 4, 6, 9, 8, 6, 8, 11, 11, 9, 10, 15, 15, 11, 14, 19, 18, 16, 19, 24, 24, 21, 24, 31, 31, 27, 32, 40, 39, 36, 41, 49, 50, 47, 52, 63, 64, 59, 67, 79, 79, 77, 85, 98, 101, 97, 106 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,16

COMMENTS

Also number of partitions of n such that if k is the largest part, then 1 occurs twice, each of 2,3,...,k-1 occurs a positive even number of times and k occurs an odd number of times. Example: a(25)=3 because we have [5,4,4,3,3,2,2,1,1], [3,3,3,3,3,2,2,2,2,1,1] and [3,2,2,2,2,2,2,2,2,2,2,1,1]. - Emeric Deutsch, Mar 29 2006

LINKS

Table of n, a(n) for n=1..83.

FORMULA

G.f.=x+sum(x^(4k)*product(1+x^(2j-1), j=1..k-1), k=1..infinity). G.f.=sum(x^(k^2)/product(1-x^(2j), j=2..k), k=1..infinity). - Emeric Deutsch, Mar 29 2006

EXAMPLE

a(25)=3 as 25=1+3+5+7+9=5+9+11=1+11+13

MAPLE

g:=sum(x^(k^2)/product(1-x^(2*j), j=2..k), k=1..10): gser:=series(g, x=0, 95): seq(coeff(gser, x, n), n=1..92); - Emeric Deutsch, Mar 29 2006

PROG

(PARI) { v=[1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 2, 1, 1, 3, 3, 1, 2, 4, 3, 2]; for (i=2, 30, c=0; forstep (j=i, 1, -2, c+=v[j]); print1(c", ")) }

CROSSREFS

a(n) = A000700(n)-A000700(n-2), n>2.

Sequence in context: A282318 A286971 A025861 * A027357 A256479 A277078

Adjacent sequences:  A090720 A090721 A090722 * A090724 A090725 A090726

KEYWORD

nonn

AUTHOR

Jon Perry, Feb 06 2004

EXTENSIONS

More terms from Vladeta Jovovic, Feb 10 2004

STATUS

approved

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