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A108404 Expansion of (1-4x)/(1-8x+11x^2). 6
1, 4, 21, 124, 761, 4724, 29421, 183404, 1143601, 7131364, 44471301, 277325404, 1729418921, 10784771924, 67254567261, 419404046924, 2615432135521, 16310012568004, 101710347053301, 634272638178364, 3955367287840601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A098648. Second binomial transform of A001077. Third binomial transform of A084057. 4th binomial transform of (1, 0, 5, 0, 25, 0, 125, 0, 625, 0, 3125, ...).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1258

Index entries for linear recurrences with constant coefficients, signature (8,-11).

FORMULA

E.g.f.: exp(4x)cosh(sqrt(5)x).

a(n) = 8a(n-1) - 11a(n-2), a(0) = 1, a(1) = 4.

a(n) = ((4+sqrt(5))^n + (4-sqrt(5))^n)/2.

a(n+1)/a(n) converges to 4 + sqrt(5) = 6.2360679774997896964... = 4+A002163.

a(n) = A091870(n+1)-4*A091870(n). - R. J. Mathar, Nov 10 2013

MATHEMATICA

CoefficientList[Series[(1-4x)/(1-8x+11x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -11}, {1, 4}, 30] (* Harvey P. Dale, Jan 03 2012 *)

CROSSREFS

Cf. A001077, A084057, A098648.

Sequence in context: A001888 A103769 A003014 * A115136 A101478 A153291

Adjacent sequences:  A108401 A108402 A108403 * A108405 A108406 A108407

KEYWORD

easy,nonn

AUTHOR

Philippe Deléham, Jul 04 2005

STATUS

approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)