OFFSET
0,2
COMMENTS
The first differences are in A122074.
a(n+1) equals the number of words of length n over {0,1,2,3,4,5,6} avoiding 01 and 02. - Milan Janjic, Dec 17 2015
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..800
Tomislav Doslic, Planar polycyclic graphs and their Tutte polynomials, Journal of Mathematical Chemistry, Volume 51, Issue 6, 2013, pp. 1599-1607.
Index entries for linear recurrences with constant coefficients, signature (7,-2).
FORMULA
G.f.: 1/(1-7*x+2*x^2).
a(n) = ((7+sqrt(41))^(1+n)-(7-sqrt(41))^(1+n))/(2^(1+n)*sqrt(41)).
a(n) = 7*a(n-1)-2*a(n-2), with a(0)=1, a(1)=7.
MATHEMATICA
CoefficientList[Series[1 / (1 - 7 x + 2 x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 19 2013 *)
LinearRecurrence[{7, -2}, {1, 7}, 30] (* Harvey P. Dale, Aug 06 2017 *)
PROG
(Magma) m:=21; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-7*x+2*x^2)));
(Magma) I:=[1, 7]; [n le 2 select I[n] else 7*Self(n-1)-2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 19 2013
(PARI) Vec(1/(1-7*x+2*x^2) + O(x^100)) \\ Altug Alkan, Dec 17 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Feb 21 2011
STATUS
approved