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A108932 Number of partitions of n into parts that are congruent to 1, 5 or 6 mod 8. 2
1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 5, 6, 7, 8, 10, 12, 13, 15, 18, 21, 24, 27, 31, 36, 41, 46, 52, 60, 68, 76, 86, 97, 109, 122, 136, 153, 172, 191, 212, 237, 264, 293, 325, 360, 400, 443, 488, 539, 596, 657, 723, 796, 876, 963, 1057, 1159, 1272, 1395, 1526, 1669, 1827 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Number of partitions of n into distinct parts that are not congruent to 3 mod 4 and the number of partitions of n into odd parts such that each part which is congruent to 3 mod 4 occurs an even number of times.

LINKS

Table of n, a(n) for n=0..60.

FORMULA

G.f.: prod_{k >= 0} 1/{(1 - x^{8k + 1})(1 - x^{8k + 5})(1 - x^{8k + 6})}.

Euler transform of period 8 sequence [1, 0, 0, 0, 1, 1, 0, 0, ...]. - Michael Somos, Jul 29 2005

PROG

(PARI) {a(n)=if(n< 0, 0, polcoeff( 1/prod(k=1, n, 1-[0, 1, 0, 0, 0, 1, 1, 0][k%8+1]*x^k, 1+x*O(x^n)), n))} /* Michael Somos, Jul 29 2005 */

CROSSREFS

Sequence in context: A029087 A177497 A029068 * A029067 A048460 A036017

Adjacent sequences:  A108929 A108930 A108931 * A108933 A108934 A108935

KEYWORD

nonn

AUTHOR

N. Sato, Jul 20 2005

STATUS

approved

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Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)