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

0,3

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

Table of n, a(n) for n=0..104.

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

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

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 *)

Crossrefs

Sequence in context: A156596 A282570 A026613 * A230632 A052511 A054533

Adjacent sequences: A117196 A117197 A117198 * A117200 A117201 A117202

Keyword

easy,nonn

Author

Paul Barry, Mar 02 2006

Extensions

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

Status

approved