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

Author

N. Sato, Jul 20 2005

Keywords

• nonn

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.

Programs

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 */

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