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Search: id:A097924
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| A097924 |
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Sequence relates numerators and denominators in the continued fraction convergents to sqrt(5). |
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+0
4
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| 2, 7, 30, 127, 538, 2279, 9654, 40895, 173234, 733831, 3108558, 13168063, 55780810, 236291303, 1000946022, 4240075391, 17961247586, 76085065735, 322301510526, 1365291107839, 5783465941882, 24499154875367, 103780085443350
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n) = A001077(n+1) - 2*A001076(n).
A048875(n) + .5(A001077(n+1)) = .5(a(n)) + A048876(n).
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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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a(n) = [(2sqrt(5)+3)*(2+sqrt(5))^n + (2sqrt(5)-3)*(2-sqrt(5))^n]/(2sqrt(5)).
a(n+1) = A001077(n+1) + A015448(n+2) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Mar 08 2005
a(n)=4*a(n-1)+a(n-2), n>1 ; a(0)=2, a(1)=7 . G.f.: (2-x)/(1-4*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 20 2008]
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MATHEMATICA
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a[n_] := Expand[((2Sqrt[5] + 3)*(2 + Sqrt[5])^n + (2Sqrt[5] - 3)*(2 - Sqrt[5])^n)/(2Sqrt[5])]; Table[ a[n], {n, 0, 20}] (from Robert G. Wilson v Sep 17 2004)
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PROGRAM
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Floretion Algebra Multiplication Program, FAMP Code: 2lesforcycseq[ ( - 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj' )*( .5'i + .5i' ) ], 2vesforcycseq = A000004. (Dement)
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CROSSREFS
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Cf. A001077, A001076.
Sequence in context: A042913 A041805 A074416 this_sequence A027136 A116363 A046648
Adjacent sequences: A097921 A097922 A097923 this_sequence A097925 A097926 A097927
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KEYWORD
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nonn
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Sep 04 2004; corrected Sep 16 2004
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EXTENSIONS
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Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2004
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