A255116 Number of n-length words on {0,1,2,3} in which 0 appears only in runs of length 2.
1, 3, 10, 33, 108, 354, 1161, 3807, 12483, 40932, 134217, 440100, 1443096, 4731939, 15516117, 50877639, 166828734, 547034553, 1793736576, 5881695930, 19286191449, 63239784075, 207364440015, 679951894392, 2229575035401, 7310818426248, 23972310961920
Offset: 0
Links
- Colin Barker, 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 10.
- Index entries for linear recurrences with constant coefficients, signature (3,0,3).
Programs
-
Mathematica
RecurrenceTable[{a[0] == 1, a[1] == 3, a[2]== 10, a[n] == 3 a[n - 1] + 3 a[n - 3]}, a[n], {n, 0, 25}] LinearRecurrence[{3,0,3},{1,3,10},30] (* Harvey P. Dale, Feb 20 2023 *) -
PARI
Vec(-(x^2+1)/(3*x^3+3*x-1) + O(x^100)) \\ Colin Barker, Feb 15 2015
Formula
a(n+3) = 3*a(n+2) + 3*a(n) with n>1, a(0) = 1, a(1) = 3, a(2) = 10.
G.f.: -(x^2+1) / (3*x^3+3*x-1). - Colin Barker, Feb 15 2015