A255632 Number of n-length words on {0,1,2,3,4} avoiding runs of zeros of length 1 (mod 3).

1, 4, 17, 73, 312, 1333, 5697, 24348, 104057, 444713, 1900592, 8122653, 34714177, 148359668, 634051937, 2709778633, 11580912872, 49493911173, 211524537857, 904002715788, 3863480419017, 16511544365353, 70566191040352

Offset: 0

Author

Milan Janjic, Feb 28 2015

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (4,0,5).

Crossrefs

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

Programs

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 4,  a[2] == 17,  a[n] == 4*a[n - 1] +  5*a[n - 3]}, a[n], {n, 0, 23}]

Formula

a(n+3) = 4*a(n+2) + 5*a(n) with n > 0, a(0) = 1, a(1) = 4, a(2) = 17.

G.f.: ( -1-x^2 ) / ( -1+4*x+5*x^3 ). - R. J. Mathar, Nov 07 2015