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A254664 Numbers of words on alphabet {0,1,...,8} with no subwords ii, where i is from {0,1,...,5}. 5
1, 9, 75, 627, 5241, 43809, 366195, 3060987, 25586481, 213874809, 1787757915, 14943687747, 124912775721, 1044133269009, 8727804479235, 72954835640907, 609822098564961, 5097441295442409, 42608996659234155, 356164297160200467 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of nonary sequences of length n such that no two consecutive terms have distance 6. - David Nacin, May 31 2017

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (8,3).

FORMULA

G.f.: (1 + x)/(1 - 8*x -3*x^2).

a(n) = 8*a(n-1) + 3*a(n-2) with n>1, a(0) = 1, a(1) = 9.

a(n) = ((1+t)*(4-t)^(n+1)+(-1+t)*(4+t)^(n+1))/(6*t), where t=sqrt(19). [Bruno Berselli, Feb 04 2015]

MATHEMATICA

RecurrenceTable[{a[0] == 1, a[1] == 9, a[n] == 8 a[n - 1] + 3 a[n - 2]}, a[n], {n, 0, 20}]

PROG

(MAGMA) [n le 1 select 9^n else 8*Self(n)+3*Self(n-1): n in [0..20]];

CROSSREFS

Cf. A015574, A055099, A126473, A126501, A126528, A254598, A254602.

Sequence in context: A125397 A095249 A190983 * A223204 A136659 A231592

Adjacent sequences:  A254661 A254662 A254663 * A254665 A254666 A254667

KEYWORD

nonn,easy

AUTHOR

Milan Janjic, Feb 04 2015

STATUS

approved

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Last modified May 18 16:07 EDT 2021. Contains 343995 sequences. (Running on oeis4.)