OFFSET
0,2
COMMENTS
Binomial transform of A085281.
Number of walks of length 2n+1 between two adjacent vertices in the cycle graph C_12. - Herbert Kociemba, Jul 05 2004
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
Mircea Merca, A Note on Cosine Power Sums J. Integer Sequences, Vol. 15 (2012), Article 12.5.3.
Index entries for linear recurrences with constant coefficients, signature (8,-19,12).
FORMULA
a(n) = 4^n/3 + 3^n/2 + 1/6.
a(n) = Sum_{k=-floor(n/6)..floor(n/6)} binomial(2*n, n+6*k)/2. - Mircea Merca, Jan 28 2012
a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) for n>2. - Colin Barker, Feb 07 2020
MATHEMATICA
CoefficientList[Series[(1 - 5*x + 5*x^2)/((1-x)*(1-3*x)*(1-4*x)), {x, 0, 50}], x] (* Stefano Spezia, Sep 09 2018 *)
PROG
(Magma) [4^n/3+3^n/2+1/6: n in [0..35]]; // Vincenzo Librandi, May 29 2011
(PARI) apply( {A085282(n)=(4^n*2+3^(n+1))\/6}, [0..29]) \\ M. F. Hasler, Feb 07 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 25 2003
STATUS
approved