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A154236
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a(n) = ((5+sqrt(6))^n-(5-sqrt(6))^n)/(2*sqrt(6)).
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1
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1, 10, 81, 620, 4661, 34830, 259741, 1935640, 14421321, 107436050, 800355401, 5962269060, 44415937981, 330876267670, 2464859855061, 18361949464880, 136787157402641, 1018994534193690, 7590989351286721, 56548997363187100
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| First differences are in A164551.
lim_{n -> infinity} a(n)/a(n-1) = 5+sqrt(6) = 7.4494897427....
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FORMULA
| a(n) = 10*a(n-1)-19*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-10x+19x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 06 2009]
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MATHEMATICA
| Join[{a=1, b=10}, Table[c=10*b-19*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 27 2011*)
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PROG
| (MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((5+r)^n-(5-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 07 2009]
(Other) Sage: [lucas_number1(n, 10, 19) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]
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CROSSREFS
| Cf. A010464 (decimal expansion of square root of 6), A164551.
Sequence in context: A010569 A136870 A018202 * A095004 A037541 A037485
Adjacent sequences: A154233 A154234 A154235 * A154237 A154238 A154239
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009
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EXTENSIONS
| Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 07 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 04 2009
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