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

0,4

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).

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

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 *)

Crossrefs

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

Sequence in context: A250415 A237040 A055284 * A081040 A102902 A127534

Adjacent sequences: A351527 A351528 A351529 * A351531 A351532 A351533

Keyword

nonn,easy

Author

R. J. Mathar, Feb 13 2022

Status

approved