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

Author

Milan Janjic, Feb 04 2015

Keywords

• nonn
• easy

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

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

Crossrefs

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

Programs

Magma

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

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 *)

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]