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A146965
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a(n) = 10*a(n-1)-18*a(n-2); a(0)=1, a(1)=5.
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2
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1, 5, 32, 230, 1724, 13100, 99968, 763880, 5839376, 44643920, 341330432, 2609713760, 19953189824, 152557050560, 1166413088768, 8918103977600, 68185604178176, 521330170184960, 3985960826642432, 30475665203095040
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The Mathematica program implements the formula provided by Deleham and Brockhaus. (* From Harvey P. Dale, Feb 17 2011 *)
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..145
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FORMULA
| a(n) = ((5+sqrt(7))^n+(5-sqrt(7))^n)/2.
G.f.: (1-5*x)/(1-10*x+18*x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 05 2008]
a(n)=(Sum_{k, 0<=k<=n}A098158(n,k)*5^(2*k)*7^(n-k)}/5^n. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 06 2008]
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MATHEMATICA
| Transpose[NestList[{#[[2]], 10#[[2]]-18#[[1]]}&, {1, 5}, 20]][[1]] (* From Harvey P. Dale, Feb 17 2011 *)
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PROG
| (MAGMA) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((5+r7)^n+(5-r7)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 05 2008]
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CROSSREFS
| Sequence in context: A199486 A065071 A153396 * A053157 A102231 A127089
Adjacent sequences: A146962 A146963 A146964 * A146966 A146967 A146968
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008
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EXTENSIONS
| Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 05 2008
Name from Philippe DELEHAM and Klaus Brockhaus, Nov 05 2008
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