A254599 Numbers of words on alphabet {0,1,...,9} with no subwords ii, for i from {0,1}.

1, 10, 98, 962, 9442, 92674, 909602, 8927810, 87627106, 860066434, 8441614754, 82855064258, 813228496354, 7981896981250, 78342900802082, 768941283068738, 7547214754035298, 74076463050867586, 727065885490090658, 7136204673817756610, 70042369148280534754

Offset

0,2

Comments

a(n) is the number of sequences over {0,1,...,9} of length n such that no two consecutive terms have distance 9. - David Nacin, May 31 2017

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,8).

Formula

a(n) = 9*a(n-1) + 8*a(n-2) with n>1, a(0) = 1, a(1) = 10.

G.f.: (1 + x)/(1 - 9*x - 8*x^2). - Bruno Berselli, Feb 02 2015

a(n) = (2^(-1-n)*((9-r)^n*(-11+r) + (9+r)^n*(11+r))) / r, where r=sqrt(113). - Colin Barker, Jan 22 2017

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 10, a[n] == 9 a[n - 1] + 8 a[n - 2]}, a[n], {n, 0, 20}] (* Bruno Berselli, Feb 02 2015 *)

Prog

(Magma) [n le 1 select 10^n else 9*Self(n)+8*Self(n-1): n in [0..20]]; // Bruno Berselli, Feb 02 2015
(PARI) Vec((1 + x)/(1 - 9*x - 8*x^2) + O(x^30)) \\ Colin Barker, Jan 22 2017

Crossrefs

Cf. A015584, A055099, A126473, A126501, A126528.

Sequence in context: A125445 A163446 A190869 * A217634 A007137 A361137

Adjacent sequences: A254596 A254597 A254598 * A254600 A254601 A254602

Keyword

nonn,easy

Author

Milan Janjic, Feb 02 2015

Status

approved