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A221286
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Vsemirnov's sequence.
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1
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106276436867, 35256392432, 141532829299, 176789221731, 318322051030, 495111272761, 813433323791, 1308544596552, 2121977920343, 3430522516895, 5552500437238, 8983022954133, 14535523391371, 23518546345504, 38054069736875, 61572616082379, 99626685819254, 161199301901633, 260825987720887, 422025289622520
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OFFSET
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0,1
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COMMENTS
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A primefree linear recurrence with no common factors. As of 2004 no such sequences with smaller starting terms were known.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
M. Vsemirnov, A new Fibonacci-like sequence of composite numbers, Journal of Integer Sequences 7:3 (2004).
Index to sequences with linear recurrences with constant coefficients, signature (1,1).
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FORMULA
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a(n) = a(n-1) + a(n-2).
G.f.: (106276436867-71020044435*x)/(1-x-x^2).
a(n) = 1/10*(-355100222175*((1/2+1/2*sqrt(5))^(n+1)+(1/2-1/2*sqrt(5))^(n+1)) +283572918169*sqrt(5)*((1/2+1/2*sqrt(5))^(n+1) -(1/2-1/2*sqrt(5))^(n+1))). [Paolo P. Lava, Feb 15 2013]
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MAPLE
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a:= n-> (<<0|1>, <1|1>>^n. <<106276436867, 35256392432>>)[1, 1]:
seq(a(n), n=0..20); # Alois P. Heinz, Apr 04 2013
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MATHEMATICA
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LinearRecurrence[{1, 1}, {106276436867, 35256392432}, 20] (* Alonso del Arte, Feb 05 2013 *)
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CROSSREFS
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Cf. A083216.
Sequence in context: A164935 A168340 A104799 * A074337 A072143 A095427
Adjacent sequences: A221283 A221284 A221285 * A221287 A221288 A221289
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KEYWORD
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nonn,easy
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AUTHOR
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Charles R Greathouse IV, Feb 05 2013
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EXTENSIONS
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Offset corrected by Alois P. Heinz, Apr 04 2013
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STATUS
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approved
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