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
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).
Programs
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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 *)
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