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

Author

Milan Janjic, Feb 28 2015

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,0,6).

Crossrefs

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

Programs

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 *)

PARI

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

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

Extensions

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