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Search: id:A015448
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| A015448 |
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Generalized Fibonacci numbers: a(n) = 4*a(n-1) + a(n-2). |
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+0
34
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| 1, 1, 5, 21, 89, 377, 1597, 6765, 28657, 121393, 514229, 2178309, 9227465, 39088169, 165580141, 701408733, 2971215073, 12586269025, 53316291173, 225851433717, 956722026041, 4052739537881, 17167680177565
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
Joerg Arndt, Fxtbook
Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n) = Fibonacci(3n+2); a(n)=[ (1+sqrt(5))(2-sqrt(5))^n - (1-sqrt(5))(2+sqrt(5))^n ]/2*sqrt(5).
O.g.f.: (1-3x)/(1-4x-x^2). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 09 2001
a(n)=Sum_{k, 0<=k<=n}3^k*A055830(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2006
a(n) = upper left term in the 2 X 2 matrix [1,2; 2,3]^n - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 02 2008
[a(n), A001076(n)] = [1,4; 1,3]^n * [1,0] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 21 2008
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MAPLE
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with(combinat): a:=n->fibonacci(n, 4)-3*fibonacci(n-1, 4): seq(a(n), n=1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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CROSSREFS
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Cf. A001076.
Sequence in context: A010925 A019992 A010917 this_sequence A099843 A035011 A113987
Adjacent sequences: A015445 A015446 A015447 this_sequence A015449 A015450 A015451
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (ogerard(AT)ext.jussieu.fr)
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