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A081192
10th binomial transform of (1,0,1,0,1,......), A059841.
6
1, 10, 101, 1030, 10601, 110050, 1151501, 12135070, 128702801, 1372684090, 14712104501, 158346365110, 1710428956601, 18532288986130, 201313313019101, 2191569650755150, 23901375026212001, 261062105099480170
OFFSET
0,2
COMMENTS
Binomial transform of A060531.
Average of binomial and inverse binomial transforms of 10^n.
a(n) is also the number of words of length n over an alphabet of eleven letters with a chosen letter appearing an even number of times. See a comment in A007582, also for the crossrefs. for the 1- to 10- letter word cases. - Wolfdieter Lang, Jul 17 2017
FORMULA
a(n) = 20*a(n-1) -99*a(n-2), a(0)=1, a(1)=10.
G.f.: (1-10*x)/((1-9*x)*(1-11*x)).
E.g.f.: exp(10*x) * cosh(x).
a(n) = 9^n/2 + 11^n/2.
a(n) = Sum_{k=0..floor(n/2)} C(n,2*k)*10^(n-2*k).
MAPLE
A081192:=n->9^n/2 + 11^n/2: seq(A081192(n), n=0..30); # Wesley Ivan Hurt, May 03 2017
MATHEMATICA
CoefficientList[Series[(1-10x)/((1-9x)(1-11x)), {x, 0, 200}], x] (* Vincenzo Librandi, Aug 07 2013 *)
PROG
(Magma) [9^n/2 + 11^n/2: n in [0..25]]; // Vincenzo Librandi, Aug 07 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 11 2003
STATUS
approved