A341307 Expansion of (x^9+x^8+2*x^7+x^6+2*x^5+2*x^4+x^3+x^2+1)/(1-x^6)^2.

1, 0, 1, 1, 2, 2, 3, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 6, 7, 6, 7, 7, 8, 8, 9, 8, 9, 9, 10, 10, 11, 10, 11, 11, 12, 12, 13, 12, 13, 13, 14, 14, 15, 14, 15, 15, 16, 16, 17, 16, 17, 17, 18, 18, 19, 18, 19, 19, 20, 20, 21, 20, 21, 21, 22, 22, 23, 22, 23, 23, 24, 24, 25, 24, 25, 25, 26, 26

Offset: 0

Author

N. J. A. Sloane, Feb 14 2021

Keywords

• nonn
• easy

Links

• Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021. I wrote 2005 on the first page but the internal evidence suggests 1997.] See page 13, top of page.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Crossrefs

Cf. A341311.

Programs

Mathematica

CoefficientList[Series[(x^9+x^8+2*x^7+x^6+2*x^5+2*x^4+x^3+x^2+1)/(1-x^6)^2,{x,0,300}],x]  (* Vincenzo Librandi, Mar 07 2021 *)

Formula

G.f.: (x^9+x^8+2*x^7+x^6+2*x^5+2*x^4+x^3+x^2+1)/(1-x^6)^2 = (1-x+x^2+x^4)/(( x-1)^2*(x+1)*(1+x+x^2)*(1-x+x^2)).

From Wesley Ivan Hurt, May 03 2021: (Start)

a(n) = floor((n+2+(-1)^n)/3).

a(n) = a(n-1)+a(n-6)-a(n-7). (End)

a(n) = A103469(n), n>=3. - R. J. Mathar, Nov 27 2023