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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

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.

Programs

Magma

A022090:= func< n | 7*Fibonacci(n) >; [A022090(n): n in [0..40]]; // G. C. Greubel, Apr 10 2025

Mathematica

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

SageMath

def A022090(n): return 7*fibonacci(n)
[A022090(n) for n in range(41)] # G. C. Greubel, Apr 10 2025

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