A255813 Numbers of words on {0,1,2,3} having no isolated zeros.

1, 3, 10, 34, 115, 388, 1309, 4417, 14905, 50296, 169720, 572707, 1932556, 6521263, 22005505, 74255899, 250570870, 845532298, 2853184279, 9627852832, 32488455385, 109629815881, 369937455865, 1248325741972, 4212380047936

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3, Example 11.

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

Formula

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

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

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 3,  a[2]== 10, a[n] == 4 a[n - 1] - 3 a[n - 2] + 3 a[n - 3]}, a[n], {n, 0, 25}]
LinearRecurrence[{4, -3, 3}, {1, 3, 10}, 100] (* G. C. Greubel, Jun 02 2016 *)

Crossrefs

Cf. A255116, A255118, A254658, A254660, A255633, A255630

Sequence in context: A255631 A289601 A291337 * A113300 A332872 A007052

Adjacent sequences: A255810 A255811 A255812 * A255814 A255815 A255816

Keyword

nonn,easy

Author

Milan Janjic, Mar 07 2015

Status

approved