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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
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
0,5
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Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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.
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
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 *)
CROSSREFS
Cf. A341311.
Sequence in context: A029209 A282630 A108309 * A103469 A337932 A029326
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 14 2021
STATUS
approved