OFFSET
0,3
COMMENTS
Counts closed walks at a vertex of the complete graph on 9 nodes K_9.
Second binomial transform is A047855.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,8).
FORMULA
G.f.: (1-7*x)/(1 - 7*x - 8*x^2).
a(n) = (8^n + 8*(-1)^n)/9.
a(n) = 8*A001045(3*n-3)/3.
From Elmo R. Oliveira, Aug 17 2024: (Start)
E.g.f.: exp(-x)*(exp(9*x) + 8)/9.
a(n) = 7*a(n-1) + 8*a(n-2) for n > 1. (End)
MATHEMATICA
k=0; lst={1, k}; Do[k=8^n-k; AppendTo[lst, k], {n, 1, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 11 2008 *)
Table[(8^n + 8*(-1)^n)/9, {n, 0, 30}] (* or *) LinearRecurrence[{7, 8}, {1, 0}, 30] (* G. C. Greubel, Jan 06 2018 *)
PROG
(Magma) [(8^n/9+8*(-1)^n/9): n in [0..20]]; // Vincenzo Librandi, Oct 11 2011
(PARI) for(n=0, 30, print1((8^n + 8*(-1)^n)/9, ", ")) \\ G. C. Greubel, Jan 06 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 23 2004
STATUS
approved