A022090 Fibonacci sequence beginning 0, 7.

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, 169104719, 273617183

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

G. C. Greubel, Table of n, a(n) for n = 0..1000

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.

Index entries for linear recurrences with constant coefficients, signature (1,1).

Formula

a(n) = round(((14*phi-7)/5) * phi^n), for n>3. - Thomas Baruchel, Sep 08 2004

a(n) = 7*Fibonacci(n) = Fibonacci(n+4) + Fibonacci(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

E.g.f.: 14*exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5). - Stefano Spezia, Nov 09 2025

Mathematica

7*Fibonacci[Range[0, 40]] (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)

Prog

(Magma)
A022090:= func< n | 7*Fibonacci(n) >; [A022090(n): n in [0..40]]; // G. C. Greubel, Apr 10 2025
(SageMath)
def A022090(n): return 7*fibonacci(n)
[A022090(n) for n in range(41)] # G. C. Greubel, Apr 10 2025

Crossrefs

Cf. A000032, A000045, A001622, A119457.

Sequences of the form Fibonacci(n+k) + Fibonacci(n-k) are listed in A280154.

Sequences of the form m*Fibonacci are listed in A022086.

Sequence in context: A168374 A112438 A309459 * A245426 A168379 A179886

Adjacent sequences: A022087 A022088 A022089 * A022091 A022092 A022093

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved