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A022090
Fibonacci sequence beginning 0, 7.
4
0, 7, 7, 14, 21, 35, 56, 91, 147, 238, 385, 623, 1008, 1631, 2639, 4270, 6909, 11179, 18088, 29267, 47355, 76622, 123977, 200599, 324576, 525175, 849751, 1374926, 2224677, 3599603, 5824280, 9423883, 15248163, 24672046, 39920209, 64592255, 104512464
OFFSET
0,2
COMMENTS
The number of heptagons in the n-th ring of the Klein Quartic. - Amiram Eldar, Nov 14 2023
REFERENCES
Arthur T. Benjamin and Jennifer J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A., 2003, p. 15.
LINKS
Tanya Khovanova, Recursive Sequences.
William P. Thurston, The Eightfold Way: A Mathematical Sculpture by Helaman Ferguson, in: The Eightfold Way: The Beauty of the Klein Quartic (ed. Silvio Levy), Cambridge University Press, New York, 1999, pp. 1-7.
Eric Weisstein's World of Mathematics, Klein Quartic.
FORMULA
a(n) = round( ((14*phi-7)/5) * phi^n) (works for n>3). - Thomas Baruchel, Sep 08 2004
a(n) = 7*F(n) = F(n+4) + F(n-4) for n>3.
a(n) = A119457(n+5,n-1) for n>1. - Reinhard Zumkeller, May 20 2006
G.f.: 7*x/(1-x-x^2). - Philippe Deléham, Nov 20 2008
MATHEMATICA
a={}; b=0; c=7; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 40, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
CROSSREFS
Cf. sequences with formula Fibonacci(n+k)+Fibonacci(n-k) listed in A280154.
Sequence in context: A168374 A112438 A309459 * A245426 A168379 A179886
KEYWORD
nonn,easy
STATUS
approved