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 A085282 Expansion of (1 - 5*x + 5*x^2)/((1-x)*(1-3*x)*(1-4*x)). 3
 1, 3, 10, 35, 126, 463, 1730, 6555, 25126, 97223, 379050, 1486675, 5858126, 23166783, 91869970, 365088395, 1453179126, 5791193143, 23100202490, 92207099715, 368247268126, 1471245680303, 5879752544610, 23503319648635 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 13 07:30 EDT 2024. Contains 375113 sequences. (Running on oeis4.)