A254664 Numbers of words on alphabet {0,1,...,8} with no subwords ii, where i is from {0,1,...,5}.

1, 9, 75, 627, 5241, 43809, 366195, 3060987, 25586481, 213874809, 1787757915, 14943687747, 124912775721, 1044133269009, 8727804479235, 72954835640907, 609822098564961, 5097441295442409, 42608996659234155, 356164297160200467

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}]
LinearRecurrence[{8, 3}, {1, 9}, 20] (* Harvey P. Dale, Feb 16 2024 *)

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 A351513 A136659

Adjacent sequences: A254661 A254662 A254663 * A254665 A254666 A254667

Keyword

nonn,easy

Author

Milan Janjic, Feb 04 2015

Status

approved