OFFSET
1,1
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..1875
Index entries for linear recurrences with constant coefficients, signature (6,-10,4).
FORMULA
a(n) = (1/4) * Sum_{r=1..7} sin(3*r*Pi/8)^2*(2*cos(r*Pi/8))^(2*n).
a(n) = 6*a(n-1) - 10*a(n-2) + 4*a(n-3), n >= 4.
G.f.: -x*(2-6*x+3*x^2) / ( (2*x-1)*(2*x^2-4*x+1) ).
a(n) = A216232(n,n), for n >= 1. - Philippe Deléham, Mar 21 2013
4*a(n) = 2*A007052(n) + 2^n. - R. J. Mathar, Nov 14 2019
MATHEMATICA
Rest@ CoefficientList[Series[-x (2 - 6 x + 3 x^2)/((2 x - 1) (2 x^2 - 4 x + 1)), {x, 0, 24}], x] (* Michael De Vlieger, Feb 12 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Herbert Kociemba, Jun 12 2004
STATUS
approved