A108932 Number of partitions of n into parts that are congruent to 1, 5 or 6 mod 8.

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

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 A351058

Adjacent sequences: A108929 A108930 A108931 * A108933 A108934 A108935

Keyword

nonn

Author

N. Sato, Jul 20 2005

Status

approved