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A254600 Numbers of words on alphabet {0,1,...,10} with no subwords ii, for i from {0,1}. 6
1, 11, 119, 1289, 13961, 151211, 1637759, 17738489, 192124721, 2080893611, 22538058599, 244108628489, 2643928812281, 28636265779211, 310158017102639, 3359306563039289, 36384487784316641, 394078636910520011, 4268246759164049879, 46229175323835178889 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) equals the number of sequences over the alphabet {0,1,...,9,10} such that no two consecutive terms have distance 10. - David Nacin, Jun 02 2017

LINKS

Colin Barker, Table of n, a(n) for n = 0..950

Index entries for linear recurrences with constant coefficients, signature (10,9).

FORMULA

G.f.: (x+1)/(1-10*x-9*x^2).

a(n) = 10*a(n-1) + 9*a(n-2) with n>1, a(0) = 1, a(1) = 11.

a(n) = ((5-sqrt(34))^n*(-6+sqrt(34)) + (5+sqrt(34))^n*(6+sqrt(34))) / (2*sqrt(34)). - Colin Barker, Jan 21 2017

MATHEMATICA

RecurrenceTable[{a[0] == 1, a[1] == 11, a[n] == 10 a[n - 1] + 9 a[n - 2]}, a[n], {n, 0, 20}]

PROG

(MAGMA) [n le 1 select 11^n else 10*Self(n)+9*Self(n-1): n in [0..20]]; // Bruno Berselli, Feb 03 2015

(PARI) Vec((x+1) / (1-10*x-9*x^2) + O(x^30)) \\ Colin Barker, Jan 21 2017

CROSSREFS

Cf. A015591, A055099, A126473, A126501, A126528.

Sequence in context: A044724 A125468 A163447 * A060499 A164828 A060498

Adjacent sequences:  A254597 A254598 A254599 * A254601 A254602 A254603

KEYWORD

nonn,easy

AUTHOR

Milan Janjic, Feb 02 2015

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)