A117199 Expansion of 1/(1-x^2) + x/(1-x^3) + x^2/(1-x^4).

1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1

Offset: 0

Author

Paul Barry, Mar 02 2006

Keywords

• easy
• nonn

Comments

Periodic {1,1,2,0,2,0,2,1,1,0,3,0}. Diagonal sums of A117198.

Number of divisors of n+2 in {2,3,4}. - Wesley Ivan Hurt, Jun 11 2023

Links

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

Programs

Mathematica

CoefficientList[ Series[1/(1 - x^2) + x/(1 - x^3) + x^2/(1 - x^4), {x, 0, 105}], x] (* Robert G. Wilson v, Mar 14 2006 *)
LinearRecurrence[{-1,-1,0,1,1,1},{1,1,2,0,2,0},120] (* or *) PadRight[ {},120,{1,1,2,0,2,0,2,1,1,0,3,0}] (* Harvey P. Dale, Dec 22 2013 *)

Formula

G.f.: (1+2x+4x^2+3x^3+3x^4)/(1+x+x^2-x^4-x^5-x^6).

a(n) = - a(n-1) - a(n-2) + a(n-4) + a(n-5) + a(n-6). - Wesley Ivan Hurt, Jun 11 2023

Extensions

More terms from Robert G. Wilson v, Mar 14 2006