OFFSET
1,2
COMMENTS
In general, a(n) = (2/m)*Sum_{r=1..m-1} sin(r*j*Pi/m)*sin(r*k*Pi/m)*(2*cos(r*Pi/m))^(2n) counts (s(0), s(1), ..., s(2n)) such that 0 < s(i) < m and |s(i)-s(i-1)| = 1 for i = 1,2,...,2n, s(0) = j, s(2n) = k.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..1825
Paul Barry, Centered polygon numbers, heptagons and nonagons, and the Robbins numbers, arXiv:2104.01644 [math.CO], 2021.
Index entries for linear recurrences with constant coefficients, signature (6,-9,1).
FORMULA
a(n) = (2/9)*Sum_{r=1..8} sin(r*Pi/3)*sin(5*r*Pi/9)*(2*cos(r*Pi/9))^(2n).
a(n) = 6a(n-1) - 9a(n-2) + a(n-3).
G.f.: (-x+2x^2)/(-1 + 6x - 9x^2 + x^3).
a(n+1) = 3*a(n) + A094832(n-1). - Philippe Deléham, Mar 20 2007
MATHEMATICA
Rest@ CoefficientList[Series[(-x + 2 x^2)/(-1 + 6 x - 9 x^2 + x^3), {x, 0, 24}], x] (* Michael De Vlieger, Jul 02 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Herbert Kociemba, Jun 13 2004
STATUS
approved