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A153882
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a(n) = ((6+sqrt(5))^n-(6-sqrt(5))^n)/(2*sqrt(5)).
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0
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1, 12, 113, 984, 8305, 69156, 572417, 4725168, 38957089, 321004860, 2644388561, 21781512072, 179402099473, 1477598319444, 12169714749665, 100231029093216, 825511191878977, 6798972400658028, 55996821859648049, 461193717895377720
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Fourth binomial transform of A048877.
First differences are in A163146.
lim_{n -> infinity} a(n)/a(n-1) = 6+sqrt(5) = 8.236067977499789696....
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FORMULA
| a(n) = 12*a(n-1)-31*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-12*x+31*x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 03 2009]
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PROG
| (MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((6+r)^n-(6-r)^n)/(2*r): n in [1..20] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
(Other) Sage: [lucas_number1(n, 12, 31) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2009]
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CROSSREFS
| Cf. A002163 (decimal expansion of sqrt(5)), A048877, A163146.
Sequence in context: A016152 A089700 A083767 * A198375 A124651 A055287
Adjacent sequences: A153879 A153880 A153881 * A153883 A153884 A153885
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jan 03 2009
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EXTENSIONS
| Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 11 2009
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