A081189 7th binomial transform of (1,0,1,0,1,...), A059841.

1, 7, 50, 364, 2696, 20272, 154400, 1188544, 9228416, 72147712, 567104000, 4476365824, 35448129536, 281408253952, 2238205337600, 17827278536704, 142148043309056, 1134363236564992, 9057979233075200, 72362273907933184

Offset: 0

Author

Paul Barry, Mar 11 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A007582, A081190.

Programs

Magma

[6^n/2 + 8^n/2: n in [0..20]]; // Vincenzo Librandi, Aug 07 2013

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 *)

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).