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Search: id:A099015
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| A099015 |
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Fib(n+1)*(2Fib(n)^2+Fib(n)Fib(n-1)+Fib(n-1)^2). |
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+0
2
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| 1, 2, 8, 33, 140, 592, 2509, 10626, 45016, 190685, 807764, 3421728, 14494697, 61400482, 260096680, 1101787113, 4667245276, 19770767984, 83750317589, 354772037730, 1502838469496, 6366125914117, 26967342128548
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Form the matrix A=[1,1,1,1;3,2,1,0;3,1,0,0;1,0,0,0]=(binomial(3-j,i)). Then a(n)=(2,2)-element of A^n.
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FORMULA
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G.f.: (1-x-4x^2)/((1+x-x^2)(1-4x-x^2))=(1-x-4x^2)/(1-3x-6x^2+3x^3+x^4); a(n)=3*Fib(3n+1)/5+(-1)^n*Fib(n-3)/5; a(n)=(2+sqrt(5))^n(3/10+3sqrt(5)/50)+(2-sqrt(5))^n(3/10-3sqrt(5)/50)+ (-1)^n((1/2-sqrt(5)/2)^n(1/5+2sqrt(5)/25)+(1/5-2sqrt(5)/25)(1/2+sqrt(5)/2)^n).
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CROSSREFS
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Cf. A000045, A056570, A066258, A066259, A099014, A033887.
Sequence in context: A134708 A037513 A037716 this_sequence A053817 A030977 A030821
Adjacent sequences: A099012 A099013 A099014 this_sequence A099016 A099017 A099018
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 22 2004
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