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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
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, ...).
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
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Jul 04 2005
STATUS
approved