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Search: id:A084128
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| A084128 |
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Generalized Fibonacci sequence. |
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+0
5
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| 1, 2, 12, 56, 272, 1312, 6336, 30592, 147712, 713216, 3443712, 16627712, 80285696, 387653632, 1871757312, 9037643776, 43637604352, 210700992512, 1017354387456, 4912221519872, 23718303629312, 114522100596736, 552961616904192
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A084058.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
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G.f.: (1-2x)/(1-4x-4x^2). E.g.f.: exp(2x)cosh(2sqrt(2)x). a(n)=4a(n-1)+4a(n-2), a(0)=1, a(1)=2; a(n)=(2+2sqrt(2))^n/2 + (2-2sqrt(2))^n/2;
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polsym(4+4*x-x^2, n)[n+1]/2)
(Other) sage: [lucas_number2(n, 4, -4)/2 for n in xrange(0, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2009]
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CROSSREFS
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Cf. A057087, A001541.
Equals 2^n * A001333(n).
Sequence in context: A020522 A037130 A078543 this_sequence A044047 A105487 A098453
Adjacent sequences: A084125 A084126 A084127 this_sequence A084129 A084130 A084131
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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), May 16 2003
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