A025796 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^6)).

1, 0, 1, 1, 1, 1, 3, 1, 3, 3, 3, 3, 6, 3, 6, 6, 6, 6, 10, 6, 10, 10, 10, 10, 15, 10, 15, 15, 15, 15, 21, 15, 21, 21, 21, 21, 28, 21, 28, 28, 28, 28, 36, 28, 36, 36, 36, 36, 45, 36, 45, 45, 45, 45, 55, 45, 55, 55, 55, 55, 66

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

Comments

Number of partitions of n into parts 2, 3, and 6. - Hoang Xuan Thanh, Aug 21 2025

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1,1,0,-1,-1,0,1).

Crossrefs

Cf. A024163.

Programs

PARI

a(n)=(n^2+(4*((n+2)%3)+7+3*(-1)^n)*n+57+33*(-1)^n/2)\72 \\ Tani Akinari, Oct 27 2014

PARI

a(n) = binomial((n\2-n%2)\3+2, 2) \\ Hoang Xuan Thanh, Aug 21 2025

Formula

a(6n) = a(6n+2) = a(6n+3) = a(6n+4) = a(6n+5) = n*(n+1)/2. a(6n+1) = (n-1)*n/2. - Franklin T. Adams-Watters, Oct 27 2014

a(n) = binomial(floor(((floor(n/2) - (n mod 2))/3)) + 2, 2). - Hoang Xuan Thanh, Aug 25 2025