A081190 8th binomial transform of (1,0,1,0,1,.....), A059841.

1, 8, 65, 536, 4481, 37928, 324545, 2803256, 24405761, 213887048, 1884629825, 16679193176, 148135411841, 1319377419368, 11777507763905, 105319346802296, 943126559710721, 8454906106826888, 75861524447454785, 681125306429182616

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

Cf. A007582, A060531, A081189.

Sequence in context: A022039 A041025 A163459 * A189431 A024105 A302316

Adjacent sequences: A081187 A081188 A081189 * A081191 A081192 A081193

Keyword

easy,nonn

Author

Paul Barry, Mar 11 2003

Status

approved