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Search: id:A099255
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| A099255 |
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G.f. (7+6*x-6*x^2-3*x^3)/((x^2+x-1)*(x^2-x-1)). |
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2
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| 7, 6, 15, 15, 38, 39, 99, 102, 259, 267, 678, 699, 1775, 1830, 4647, 4791, 12166, 12543, 31851, 32838, 83387, 85971, 218310, 225075, 571543, 589254, 1496319, 1542687, 3917414, 4038807, 10255923, 10573734, 26850355, 27682395, 70295142, 72473451
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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. "pos((Ex)^n)" sums up over all floretion basis vectors with positive coefficients for each n. The following relations appear to hold: a(2n) - (a(2n-1) + a(2n-2)) = 2*Luc(2n) a(2n+1) - a(2n) = Fib(2n), apart from initial term a(2n+1)/a(2n-1) -> 2 + golden ratio phi a(2n)/a(2n-2) -> 2 + golden ratio phi An identity: (1/2)a(n) - (1/2)A099256(n) = ((-1)^n)A000032(n)
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FORMULA
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a(n) = 2*pos((Ex)^n)
a(0) = 7, a(1) = 6, a(2) = a(3) = 15, a(n+4) = 3a(n+2) - a(n).
a(2n) = A022097(2n+1), a(2n+1) = A022086(2n+3).
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PROGRAM
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Floretion Algebra Multiplication Program, FAMP
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CROSSREFS
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Cf. A099256, A000032.
Adjacent sequences: A099252 A099253 A099254 this_sequence A099256 A099257 A099258
Sequence in context: A085964 A082121 A078323 this_sequence A073112 A070425 A038272
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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), Oct 09 2004
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EXTENSIONS
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More terms from Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Apr 19 2005
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