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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, 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
0,4
FORMULA
a(n) = Sum_{i=1..n} A001906(n-i) * A052921(i-1).
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
EXAMPLE
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.
CROSSREFS
Sequence in context: A128553 A190163 A364553 * A235612 A000340 A301880
KEYWORD
nonn,easy
AUTHOR
Mauricio J. Santos, Sep 15 2020
EXTENSIONS
a(20)-a(29) from Alois P. Heinz, Sep 15 2020
STATUS
approved