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A154347
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a(n) = ((7+2*sqrt(2))^n-(7-2*sqrt(2))^n)/(4*sqrt(2)).
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0
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1, 14, 155, 1596, 15989, 158410, 1562191, 15375864, 151212265, 1486561286, 14612155139, 143621159220, 1411597868381, 13873902629314, 136359124206775, 1340197731092976, 13172044142823889, 129460511024722430
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Fourth binomial transform of A054489.
lim_{n -> infinity} a(n)/a(n-1) = 7+2*sqrt(2) = 9.8284271247....
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FORMULA
| a(n) = 14*a(n-1)-41*a(n-2) for n>1; a(0)=0, a(1)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 12 2009]
G.f.: x/(1-14*x+41*x^2). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 12 2009, corrected Oct 08 2009]
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MATHEMATICA
| Join[{a=1, b=14}, Table[c=14*b-41*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 01 2011*)
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PROG
| (MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((7+2*r)^n-(7-2*r)^n)/(4*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 12 2009]
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CROSSREFS
| Cf. A002193 (decimal expansion of sqrt(2)), A054489.
Sequence in context: A004986 A154248 A006865 * A001707 A078999 A016157
Adjacent sequences: A154344 A154345 A154346 * A154348 A154349 A154350
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
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EXTENSIONS
| Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 12 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 08 2009
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