A078657 Expansion of 1/Product_{ n >= 2, n not of the form 2^k-1 } (1 - x^n).

1, 0, 1, 0, 2, 1, 3, 1, 5, 3, 8, 5, 12, 9, 18, 14, 27, 23, 40, 35, 58, 54, 84, 80, 120, 118, 170, 171, 239, 246, 334, 347, 463, 489, 638, 680, 873, 940, 1189, 1288, 1609, 1755, 2167, 2374, 2903, 3196, 3872, 4275, 5140, 5692, 6795, 7540, 8944, 9945, 11729, 13057, 15321, 17077

Offset

0,5

Comments

a(n) counts the partitions of n where no part has the form 2^k - 1 for a positive integer k. - Brian Hopkins, Jul 21 2017

Links

Table of n, a(n) for n=0..57.

Example

The a(9) = 3 allowed partitions of 9 are (9), (5,4), and (5,2,2).

Prog

(PARI) isok(p) = {for (i=1, #p, if ((p[i]==1) || (ispower(p[i]+1, , &t) && (t==2)), return (0)); ); return(1); }
a(n) = {my(nb = 0); forpart(p=n, nb += isok(p); ); nb; } \\ Michel Marcus, Jul 22 2017

Crossrefs

Cf. A078658.

Sequence in context: A330547 A338357 A338358 * A080959 A065548 A152063

Adjacent sequences: A078654 A078655 A078656 * A078658 A078659 A078660

Keyword

nonn

Author

N. J. A. Sloane, Dec 15 2002

Status

approved