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Search: id:A159289
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| A159289 |
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a(n+1) = 5*a(n) - 2*a(n-1) |
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+0
1
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| 5, 21, 95, 433, 1975, 9009, 41095, 187457, 855095, 3900561, 17792615, 81161953, 370224535, 1688798769, 7703544775, 35140126337, 160293542135, 731187458001, 3335350205735, 15214376112673, 69401180151895, 316577148534129
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Generating floretion: E*X with E = 0.25('i + i' + 'ii' + 'jj' + 'kk' + jk' + 'kj' + 1) and X = -'i + 'j - 4i' + 'ij' + 'ik' The sequence appears to be related to "Kekule numbers for certain benzenoids": (a(n)) = 2diaKtesseq[E*X], A052984 = 2diaJtesseq[E*X], A107839 = -1diaItesseq[E*X]
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LINKS
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Creighton Dement, Online Floretion Multiplier
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FORMULA
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G.f.: -(-5+4*x)/(1-5*x+2*x^2). a(n) = 5*A107839(n)-4*A107839(n-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 10 2009]
a(n)=(5/2)*{[(5/2)+(1/2)*sqrt(17)]^n+[(5/2)-(1/2)*sqrt(17)]^n} +(1/2)*sqrt(17)*{[(5/2)+(1/2)*sqrt(17)]^n-[(5/2)-(1/2)*sqrt(17)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Jul 31 2009]
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CROSSREFS
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A052984, A107839
Sequence in context: A116904 A126952 A103519 this_sequence A017968 A017969 A050897
Adjacent sequences: A159286 A159287 A159288 this_sequence A159290 A159291 A159292
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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), Apr 08 2009
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