A085282 Expansion of (1 - 5*x + 5*x^2)/((1-x)*(1-3*x)*(1-4*x)).

1, 3, 10, 35, 126, 463, 1730, 6555, 25126, 97223, 379050, 1486675, 5858126, 23166783, 91869970, 365088395, 1453179126, 5791193143, 23100202490, 92207099715, 368247268126, 1471245680303, 5879752544610, 23503319648635

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

Sequence in context: A088218 A300975 A072266 * A149036 A316596 A047127

Adjacent sequences: A085279 A085280 A085281 * A085283 A085284 A085285

Keyword

easy,nonn

Author

Paul Barry, Jun 25 2003

Status

approved