A255631 Number of n-length words on {0,1,2,3} avoiding runs of zeros of length 1 (mod 3).

1, 3, 10, 34, 114, 382, 1282, 4302, 14434, 48430, 162498, 545230, 1829410, 6138222, 20595586, 69104398, 231866082, 777980590, 2610359362, 8758542414, 29387549602, 98604086254, 330846428418, 1110089483662, 3724684796002, 12497440101678, 41932678239682

Offset: 0

Author

Milan Janjic, Feb 28 2015

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,4).

Crossrefs

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

Programs

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 3,  a[2] == 10,  a[n] == 3* a[n - 1] +  4*a[n - 3]}, a[n], {n, 0, 25}]
LinearRecurrence[{3,0,4},{1,3,10},40] (* Harvey P. Dale, Aug 01 2021 *)

Formula

a(n+3) = 3*a(n+2) + 4*a(n) with n > 0, a(0) = 1, a(1) = 3, a(2) = 10.

G.f.: -(x^2+1) / (4*x^3+3*x-1). - Colin Barker, Mar 20 2015