A051263 Expansion of 1/((1-x)*(1-x^3)^2*(1-x^5)).

1, 1, 1, 3, 3, 4, 7, 7, 9, 13, 14, 17, 22, 24, 28, 35, 38, 43, 52, 56, 63, 74, 79, 88, 101, 108, 119, 134, 143, 156, 174, 185, 200, 221, 234, 252, 276, 291, 312, 339, 357, 381, 411, 432, 459, 493, 517, 547, 585, 612, 646, 688, 718, 756, 802, 836, 878, 928, 966

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

A two-way infinite sequences which is palindromic (up to sign). - Michael Somos, Mar 21 2003

Links

• Index entries for two-way infinite sequences
• Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,1,-2,1,-2,2,0,1,-1).

Crossrefs

Cf. A028242, A028288, A029153.

Programs

PARI

{a(n) = if( n<-11, -a(-12 - n), if( n<0, 0, polcoeff( 1 / ((1 - x) * (1 - x^3)^2 * (1 - x^5)) + x * O(x^n),n)))} /* Michael Somos, Mar 21 2003 */

Formula

G.f.: 1 / ((1 - x) * (1 - x^3)^2 * (1 - x^5)).

a(-12 - n) = -a(n). a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) + a(n-5) - 2*a(n-6) + a(n-7) - 2*a(n-8) + 2*a(n-9) + a(n-11) - a(n-12). - Michael Somos, Mar 21 2003

A029153(n) = a(floor(n/2) - mod(n,2)) = a(A028242(n - 2)). - Michael Somos, Mar 21 2003

a(n) = 1 + [(n mod 15)=6] + floor((n^3+18*n^2+(87+30*[(n mod 3)=0])*n)/270) where [] is Iverson bracket. - Hoang Xuan Thanh, Jun 06 2025