OFFSET
0,1
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).
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
MATHEMATICA
CoefficientList[Series[(2 + 9 x)/(1 - x - x^2), {x, 0, 40}], x] (* Wesley Ivan Hurt, Jun 15 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 14 1998
STATUS
approved