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A022115 Fibonacci sequence beginning 2, 11.

%I A022115 #49 Feb 14 2025 17:24:43
%S A022115 2,11,13,24,37,61,98,159,257,416,673,1089,1762,2851,4613,7464,12077,
%T A022115 19541,31618,51159,82777,133936,216713,350649,567362,918011,1485373,
%U A022115 2403384,3888757,6292141,10180898,16473039,26653937,43126976,69780913,112907889,182688802
%N A022115 Fibonacci sequence beginning 2, 11.
%C A022115 For n >= 1, a(n) is the number of edge covers of the tadpole graph T_{5,n-1} with T_{5,0} interpreted as just the cycle graph C_5. Example: If n=2, we have C_5 and path P_1 joined by a bridge. This is the cycle C_5 with a pendant and has 13 edge covers. - _Feryal Alayont_, Sep 22 2024
%H A022115 Ivan Panchenko, <a href="/A022115/b022115.txt">Table of n, a(n) for n = 0..1000</a>
%H A022115 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A022115 Clark Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/52-5/Problems.pdf">Problem Proposals</a>, The Fibonacci Quarterly, vol. 52 #5, 2015, p5-14.
%H A022115 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TadpoleGraph.html">Tadpole Graph</a>.
%H A022115 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A022115 G.f.: (2+9*x)/(1-x-x^2). - _Philippe Deléham_, Nov 19 2008
%F A022115 a(n) = 12*F(n) + F(n-3). - _J. M. Bergot_, Jul 20 2017
%F A022115 a(n) = 8*F(n) + F(n+3). - _Feryal Alayont_, Sep 22 2024
%t A022115 CoefficientList[Series[(2 + 9 x)/(1 - x - x^2), {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Jun 15 2014 *)
%t A022115 LinearRecurrence[{1,1},{2,11},40] (* _Harvey P. Dale_, Feb 14 2025 *)
%Y A022115 Cf. A000032, A000045.
%K A022115 nonn,easy
%O A022115 0,1
%A A022115 _N. J. A. Sloane_, Jun 14 1998