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A108404
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Expansion of (1-4x)/(1-8x+11x^2).
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3
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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; internal format)
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OFFSET
| 0,2
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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, ...).
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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...
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MATHEMATICA
| CoefficientList[Series[(1-4x)/(1-8x+11x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -11}, {1, 4}, 30] (* From Harvey P. Dale, Jan 03 2012 *)
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CROSSREFS
| Cf. A001077, A084057, A098648.
Sequence in context: A001888 A103769 A003014 * A115136 A101478 A153291
Adjacent sequences: A108401 A108402 A108403 * A108405 A108406 A108407
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KEYWORD
| easy,nonn
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 04 2005
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