|
%I #33 Nov 14 2023 04:36:42
%S 0,7,7,14,21,35,56,91,147,238,385,623,1008,1631,2639,4270,6909,11179,
%T 18088,29267,47355,76622,123977,200599,324576,525175,849751,1374926,
%U 2224677,3599603,5824280,9423883,15248163,24672046,39920209,64592255,104512464
%N Fibonacci sequence beginning 0, 7.
%C The number of heptagons in the n-th ring of the Klein Quartic. - _Amiram Eldar_, Nov 14 2023
%D Arthur T. Benjamin and Jennifer J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A., 2003, p. 15.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H William P. Thurston, <a href="https://people.eecs.berkeley.edu/~sequin/CS285/PAPERS/thurston.pdf">The Eightfold Way: A Mathematical Sculpture by Helaman Ferguson</a>, in: The Eightfold Way: The Beauty of the Klein Quartic (ed. Silvio Levy), Cambridge University Press, New York, 1999, pp. 1-7.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KleinQuartic.html">Klein Quartic</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F a(n) = round( ((14*phi-7)/5) * phi^n) (works for n>3). - _Thomas Baruchel_, Sep 08 2004
%F a(n) = 7*F(n) = F(n+4) + F(n-4) for n>3.
%F a(n) = A119457(n+5,n-1) for n>1. - _Reinhard Zumkeller_, May 20 2006
%F G.f.: 7*x/(1-x-x^2). - _Philippe Deléham_, Nov 20 2008
%t 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 *)
%Y Cf. A000032, A000045, A001622, A119457.
%Y Cf. sequences with formula Fibonacci(n+k)+Fibonacci(n-k) listed in A280154.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
|
