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

0,2

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (20,-99).

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

Cf. A007582, A059841, A060531.

Sequence in context: A041041 A333344 A163461 * A288809 A288895 A290201

Adjacent sequences: A081189 A081190 A081191 * A081193 A081194 A081195

Keyword

easy,nonn

Author

Paul Barry, Mar 11 2003

Status

approved