A255633 Number of n-length words on {0,1,2,3,4,5} avoiding runs of zeros of length 1 (mod 3).

1, 5, 26, 136, 710, 3706, 19346, 100990, 527186, 2752006, 14365970, 74992966, 391476866, 2043580150, 10667858546, 55688153926, 290702250530, 1517518403926, 7921720943186, 41352818219110, 215869201519106, 1126876333254646, 5882498575587890, 30707708087054086

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,0,6).

Formula

a(n+3) = 5*a(n+2) + 6*a(n) with n > 0, a(0) = 1, a(1) = 5, a(2) = 26.

G.f.: (1 + x^2)/(1 - 5*x - 6*x^3). - Andrew Howroyd, May 01 2020

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 5,  a[2] == 26,  a[n] == 5* a[n - 1] +  6*a[n - 3]}, a[n], {n, 0, 20}]
LinearRecurrence[{5, 0, 6}, {1, 5, 26}, 30] (* Harvey P. Dale, Aug 11 2023 *)

Prog

(PARI) Vec((1 + x^2)/(1 - 5*x - 6*x^3) + O(x^30)) \\ Andrew Howroyd, May 01 2020

Crossrefs

Cf. A254598, A254602, A255115, A255117, A254601, A254663.

Sequence in context: A022032 A255118 A052918 * A255815 A018903 A355361

Adjacent sequences: A255630 A255631 A255632 * A255634 A255635 A255636

Keyword

nonn,easy

Author

Milan Janjic, Feb 28 2015

Extensions

Terms a(20) and beyond from Andrew Howroyd, May 01 2020

Status

approved