A153709 Expansion of (1 + 7*x)/(1 - 11*x - 26*x^2).

1, 18, 224, 2932, 38076, 495068, 6435724, 83664732, 1087640876, 14139332668, 183811322124, 2389547192732, 31064113495276, 403833475459068, 5249835180926924, 68247857352131932, 887222145577551276, 11533887892508494268, 149940542602609770124, 1949227053833928322332

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Tomislav Došlić and Frode Måløy, Chain hexagonal cacti: Matchings and independent sets, Discr. Math., 310 (2010), 1676-1690.

Index entries for linear recurrences with constant coefficients, signature (11,26).

Formula

From G. C. Greubel, Aug 25 2016: (Start)

a(n) = (4*(13)^n - (-2)^n)/3.

a(n) = 11*a(n-1) + 26*a(n-2).

E.g.f.: (1/3)*(4*exp(13*x) - exp(-2*x)). (End)

Mathematica

CoefficientList[Series[(1+7x)/(1-11x-26x^2), {x, 0, 25}], x]  (* Harvey P. Dale, Feb 23 2011 *)
LinearRecurrence[{11, 26}, {1, 18}, 25] (* or *) Table[(4*(13)^n - (-2)^n)/3, {n, 0, 20}] (* G. C. Greubel, Aug 25 2016 *)

Prog

(Magma) [(4*(13)^n - (-2)^n)/3: n in [1..25]]; // Vincenzo Librandi, Aug 26 2016
(PARI) Vec((1+7*x)/(1-11*x-26*x^2) + O(x^99)) \\ Altug Alkan, Aug 26 2016

Crossrefs

Sequence in context: A021194 A155049 A155073 * A017933 A021384 A056950

Adjacent sequences: A153706 A153707 A153708 * A153710 A153711 A153712

Keyword

nonn,easy

Author

N. J. A. Sloane, May 22 2010

Status

approved