A254659 Numbers of words on alphabet {0,1,...,8} with no subwords ii, where i is from {0,1,2,3}.

1, 9, 77, 661, 5673, 48689, 417877, 3586461, 30781073, 264180889, 2267352477, 19459724261, 167014556473, 1433415073089, 12302393367077, 105586222302061, 906201745251873, 7777545073525289, 66751369314461677, 572898679883319861, 4916946285638867273

Offset

0,2

Comments

a(n) is the number of nonary sequences of length n such that no two consecutive terms have distance 7. - 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 (8,5).

Formula

G.f.: (1 + x)/(1 - 8*x - 5*x^2).

a(n) = 8*a(n-1) + 5*a(n-2) with n>1, a(0) = 1, a(1) = 9.

a(n) = ((4-r)^n*(-5+r) + (4+r)^n*(5+r)) / (2*r), where r=sqrt(21). - Colin Barker, Jan 22 2017

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 9, a[n] == 8 a[n - 1] + 5 a[n - 2]}, a[n], {n, 0, 20}]

Prog

(Magma) [n le 1 select 9^n else 8*Self(n)+5*Self(n-1): n in [0..20]];
(PARI) Vec((1 + x)/(1 - 8*x -5*x^2) + O(x^30)) \\ Colin Barker, Jan 22 2017

Crossrefs

Cf. A015575, A055099, A126473, A126501, A126528, A254598, A254602.

Sequence in context: A290708 A126631 A190981 * A346847 A355372 A046150

Adjacent sequences: A254656 A254657 A254658 * A254660 A254661 A254662

Keyword

nonn,easy

Author

Milan Janjic, Feb 04 2015

Status

approved