A351530 The number of quinary strings of length n containing 00.

0, 0, 1, 9, 65, 421, 2569, 15085, 86241, 483429, 2669305, 14564061, 78699089, 421880725, 2246459881, 11894065549, 62665617345, 328756309701, 1718275598809, 8951067087165, 46492068009521, 240846026714869, 1244719810538185, 6419100507215341

Offset: 0

Author

R. J. Mathar, Feb 13 2022

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1430
• Index entries for linear recurrences with constant coefficients, signature (9,-16,-20).

Crossrefs

Cf. A008466 (2-ary), A186244 (3-ary), A351529 (4-ary), A086347 (not containing 00).

Programs

Mathematica

CoefficientList[Series[x^2/((5*x - 1)*(4*x^2 + 4*x - 1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jun 22 2022 *)
LinearRecurrence[{9,-16,-20},{0,0,1},30] (* Harvey P. Dale, Mar 26 2024 *)

Formula

G.f.: x^2 / ( (5*x-1)*(4*x^2+4*x-1) ).

a(n) = 5^n - A086347(n).

a(n) = 9*a(n-1) - 16*a(n-2) - 20*a(n-3). - Wesley Ivan Hurt, Jun 22 2022