OFFSET
0,2
COMMENTS
Binomial transform of A081189.
a(n) is also the number of words of length n over an alphabet of nine letters, of which a chosen one appears an even number of times. See a comment in A007582, also for the crossrefs. for the 1- to 11- letter word cases. For a formulation in terms of maps see a Geoffrey Critzer comment in A081189. - 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 (16,-63).
FORMULA
a(n) = 16*a(n-1) -63*a(n-2), a(0)=1, a(1)=8.
G.f.: (1-8*x)/((1-7*x)*(1-9*x)).
E.g.f. exp(8*x) * cosh(x).
a(n) = 7^n/2 + 9^n/2.
MATHEMATICA
CoefficientList[Series[(1 - 8 x) / ((1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)
LinearRecurrence[{16, -63}, {1, 8}, 20] (* Harvey P. Dale, Apr 04 2017 *)
PROG
(Magma) [7^n/2 + 9^n/2: n in [0..25]]; // Vincenzo Librandi, Aug 07 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 11 2003
STATUS
approved