OFFSET
0,2
COMMENTS
Binomial transform of A081188.
a(n) is the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7,8} with an even number of elements mapped to 1. - Geoffrey Critzer, Dec 30 2012
For the alternative formulation in terms of words of length n over an alphabet of eight letters with a chosen letter appearing an even number of times see a comment in A007582, also for the crossrefs, for the 1- to 11- letter word cases. - Wolfdieter Lang, Jul 17 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (14,-48).
FORMULA
a(n) = 14*a(n-1) - 48*a(n-2) with n > 1, a(0)=1, a(1)=7.
G.f.: (1-7*x)/((1-6*x)*(1-8*x)).
E.g.f. exp(7*x)*cosh(x).
a(n) = 6^n/2 + 8^n/2.
a(n) = 6*a(n-1) + 8^(n-1).
MATHEMATICA
nn=20; Range[0, nn]!CoefficientList[Series[Exp[7x]Cosh[x], {x, 0, nn}], x] (* Geoffrey Critzer, Dec 30 2012 *)
LinearRecurrence[{14, -48}, {1, 7}, 20] (* Or *)
CoefficientList[Series[(1 - 7 x)/(1 - 14 x + 48 x^2), {x, 0, 19}], x] (* Robert G. Wilson v, Jan 02 2013 *)
PROG
(Magma) [6^n/2 + 8^n/2: n in [0..20]]; // Vincenzo Librandi, Aug 07 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 11 2003
STATUS
approved