A081192 10th binomial transform of (1,0,1,0,1,......), A059841.

1, 10, 101, 1030, 10601, 110050, 1151501, 12135070, 128702801, 1372684090, 14712104501, 158346365110, 1710428956601, 18532288986130, 201313313019101, 2191569650755150, 23901375026212001, 261062105099480170

Offset: 0

Author

Paul Barry, Mar 11 2003

Keywords

• easy
• nonn

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (20,-99).

Crossrefs

Cf. A007582, A059841, A060531.

Programs

Magma

[9^n/2 + 11^n/2: n in [0..25]]; // Vincenzo Librandi, Aug 07 2013

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 *)

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).