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A099256
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G.f.: (3-x)(1+3x+x^2)/((1-x-x^2)(1+x-x^2)).
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2
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3, 8, 9, 23, 24, 61, 63, 160, 165, 419, 432, 1097, 1131, 2872, 2961, 7519, 7752, 19685, 20295, 51536, 53133, 134923, 139104, 353233, 364179, 924776, 953433, 2421095, 2496120, 6338509, 6534927, 16594432, 17108661, 43444787, 44791056, 113739929, 117264507, 297775000, 307002465, 779585071
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| One of two sequences involving the Lucas/Fibonacci numbers. This sequence consists of pairs of numbers more or less close to each other with "jumps" in between pairs.
a(n+3) + a(n) - a(n+2) appears to be mysteriously connected with a(n+1).
Both this sequence and A099255 were created using "Floretion dynamical symmetries" (see link for further details).
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(2n+2) - a(2n+1) = F(2n-1).
An identity: (1/2)A099255(n) - (1/2)a(n) = ((-1)^n)A000032(n)
a(0) = 3, a(1) = 8, a(2) = 9, a(3) = 23, a(n+4) = 3a(n+2) - a(n).
a(2n) = A022086(2n+2), a(2n+1) = A022097(2n+2).
a(n) = A013655(n+2)-A061084(n+1).
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PROG
| Floretion Algebra Multiplication Program, FAMP
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CROSSREFS
| Cf. A099255, A000032.
Sequence in context: A080517 A191487 A176205 * A167344 A025615 A101720
Adjacent sequences: A099253 A099254 A099255 * A099257 A099258 A099259
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KEYWORD
| nonn
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 18 2004
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EXTENSIONS
| Definition corrected, extended. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 13 2008
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