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 A016208 Expansion of 1/((1-x)*(1-3*x)*(1-4*x)). 8
 1, 8, 45, 220, 1001, 4368, 18565, 77540, 320001, 1309528, 5326685, 21572460, 87087001, 350739488, 1410132405, 5662052980, 22712782001, 91044838248, 364760483725, 1460785327100, 5848371485001, 23409176469808, 93683777468645, 374876324642820, 1499928942876001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A085277. - Paul Barry, Jun 25 2003 Number of walks of length 2n+5 between two nodes at distance 5 in the cycle graph C_12. - Herbert Kociemba, Jul 05 2004 LINKS Index entries for linear recurrences with constant coefficients, signature (8,-19,12) FORMULA a(n) = 16*4^n/3 + 1/6 - 9*3^n/2. - Paul Barry, Jun 25 2003 a(0) = 0, a(1) = 8, a(n) = 7*a(n-1) - 12*a(n-2) + 1. - Vincenzo Librandi, Feb 10 2011 a(0) = 1, a(1) = 8, a(2) = 45, a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3). - Harvey P. Dale, Apr 09 2012 MATHEMATICA Table[(2^(2*n + 3) - 3^(n + 2) + 1)/6, {n, 40}] (* Vladimir Joseph Stephan Orlovsky, Jan 19 2011 *) CoefficientList[Series[1/((1-x)(1-3x)(1-4x)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {8, -19, 12}, {1, 8, 45}, 30] (* Harvey P. Dale, Apr 09 2012 *) PROG (PARI) Vec(1/((1-x)*(1-3*x)*(1-4*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012 CROSSREFS Cf. A000225, A000295, A000392, A002275, A003462, A003463, A003464, A023000, A023001, A002452, A016123, A016125, A016256. Sequence in context: A273305 A026015 A002696 * A216540 A026852 A110609 Adjacent sequences:  A016205 A016206 A016207 * A016209 A016210 A016211 KEYWORD nonn,easy AUTHOR STATUS approved

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