A335551 Number of words of length n over the alphabet {0,1,2} that contain the substring 12 but not the substring 01.
0, 0, 1, 5, 18, 58, 177, 522, 1503, 4252, 11869, 32787, 89821, 244415, 661415, 1781654, 4780776, 12786704, 34104792, 90749209, 240982564, 638800052, 1690764378, 4469170031, 11799684559, 31122693066, 82016622160, 215969175981, 568313267862, 1494601936229
Offset: 0
Examples
a(0) = a(1) = 0, because no word of length n < 2 can contain 12. a(2) = 1, because there is one word of length 2 and it is 12. a(3) = 5, because there are 5 words of length 3 and they are 121, 112, 212, 122, 120.
Links
- Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-5,1).
Formula
G.f.: x^2*(x-1)/((x^2-3*x+1)*(x^3-2*x^2+3*x-1)). - Alois P. Heinz, Sep 15 2020
Extensions
a(20)-a(29) from Alois P. Heinz, Sep 15 2020