A395831 Number of octal strings of length n that do not contain a specific string xx (where x is a single digit).

1, 8, 63, 497, 3920, 30919, 243873, 1923544, 15171919, 119668241, 943881120, 7444845527, 58721086529, 463161524392, 3653178276447, 28814378605873, 227272898176240, 1792610937474791, 14139186849557217, 111522584509224056, 879632399511468911, 6938084888144850769

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (7,7).

Formula

a(n) = 8^n - A340156(8,n).

a(n) = 8^n - A395829(n).

G.f.: -(x + 1)/(7*x^2 + 7*x - 1). - Amiram Eldar, May 16 2026

Mathematica

LinearRecurrence[{7, 7}, {1, 8}, 22] (* Amiram Eldar, May 16 2026 *)

Prog

(PARI) Vec(-(x + 1)/(7*x^2 + 7*x - 1) + O(x^22))

Crossrefs

Cf. A340156, A395829.

Cf. A000045, A028859, A125145, A086347, A180033, A180167, A322054, A395832.

Sequence in context: A164592 A242631 A001090 * A387841 A390821 A243782

Adjacent sequences: A395828 A395829 A395830 * A395832 A395833 A395834

Keyword

nonn,easy

Author

A.H.M. Smeets, May 16 2026

Status

approved