OFFSET
1,1
COMMENTS
Each term of this sequence beyond the sixth has a primitive prime divisor. - Anthony Flatters (Anthony.Flatters(AT)uea.ac.uk), Aug 17 2007
a(n) is also the number of spanning trees for the n-gear graph. - Eric W. Weisstein, Jul 16 2011
LINKS
Stefano Spezia, Table of n, a(n) for n = 1..1700
G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.
Anthony Flatters, Primitive Divisors of some Lehmer-Pierce Sequences, arXiv:0708.2190 [math.NT], 2007.
Eric Weisstein's World of Mathematics, Gear Graph
Eric Weisstein's World of Mathematics, Spanning Tree
Index entries for linear recurrences with constant coefficients, signature (5,-5,1).
FORMULA
a(n) = 2*A092184(n). - Robert G. Wilson v, Jul 04 2007
O.g.f.: 2*x*(1+x)/((1-x)*(1-4*x+x^2)). - R. J. Mathar, Dec 05 2007
a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3). - Eric W. Weisstein, Jul 15 2011
E.g.f.: 2*exp(x)*(exp(x)*cosh(sqrt(3)*x) - 1). - Stefano Spezia, May 05 2024
MAPLE
u:=2+sqrt(3): v:=2-sqrt(3): a:=n->expand(-(u^n-1)*(v^n-1)): seq(a(n), n=1..28); # Emeric Deutsch, May 13 2007
MATHEMATICA
Table[-((2 + Sqrt[3])^n - 1)*((2 - Sqrt[3])^n - 1)], {n, 30}] // Expand (* Stefan Steinerberger, May 15 2007 *)
LinearRecurrence[{5, -5, 1}, {2, 12, 50}, 30]
LucasL[2 Range[20], Sqrt[2]] - 2 // Round (* Eric W. Weisstein, Mar 28 2018 *)
PROG
(PARI) x='x+O('x^99); Vec(2*x*(1+x)/((1-x)*(1-4*x+x^2))) \\ Altug Alkan, Mar 28 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 13 2007
EXTENSIONS
More terms from Emeric Deutsch and Stefan Steinerberger, May 13 2007
More terms from Vladeta Jovovic, May 30 2007
STATUS
approved