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

0,2

Links

Table of n, a(n) for n=0..22.

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

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

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}]

Crossrefs

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

Sequence in context: A085732 A289159 A083330 * A255814 A095940 A018902

Adjacent sequences: A255629 A255630 A255631 * A255633 A255634 A255635

Keyword

nonn,easy

Author

Milan Janjic, Feb 28 2015

Status

approved