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

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,4).

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

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 *)

Crossrefs

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

Sequence in context: A034215 A193036 A083580 * A289601 A291337 A255813

Adjacent sequences: A255628 A255629 A255630 * A255632 A255633 A255634

Keyword

nonn,easy

Author

Milan Janjic, Feb 28 2015

Status

approved