A108404 Expansion of (1-4x)/(1-8x+11x^2).

1, 4, 21, 124, 761, 4724, 29421, 183404, 1143601, 7131364, 44471301, 277325404, 1729418921, 10784771924, 67254567261, 419404046924, 2615432135521, 16310012568004, 101710347053301, 634272638178364, 3955367287840601

Offset: 0

Author

Philippe Deléham, Jul 04 2005

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A001077, A084057, A098648.

Programs

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 *)

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