A022115 Fibonacci sequence beginning 2, 11.

2, 11, 13, 24, 37, 61, 98, 159, 257, 416, 673, 1089, 1762, 2851, 4613, 7464, 12077, 19541, 31618, 51159, 82777, 133936, 216713, 350649, 567362, 918011, 1485373, 2403384, 3888757, 6292141, 10180898, 16473039, 26653937, 43126976, 69780913, 112907889, 182688802

Offset: 0

Author

N. J. A. Sloane, Jun 14 1998

Keywords

• nonn
• easy

Comments

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

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences
• Clark Kimberling, Problem Proposals, The Fibonacci Quarterly, vol. 52 #5, 2015, p5-14.
• Eric Weisstein's World of Mathematics, Tadpole Graph.
• Index entries for linear recurrences with constant coefficients, signature (1,1).

Crossrefs

Cf. A000032, A000045.

Programs

Mathematica

CoefficientList[Series[(2 + 9 x)/(1 - x - x^2), {x, 0, 40}], x] (* Wesley Ivan Hurt, Jun 15 2014 *)
LinearRecurrence[{1,1},{2,11},40] (* Harvey P. Dale, Feb 14 2025 *)

Formula

G.f.: (2+9*x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = 12*F(n) + F(n-3). - J. M. Bergot, Jul 20 2017

a(n) = 8*F(n) + F(n+3). - Feryal Alayont, Sep 22 2024