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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-5,1).

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

Cf. A001906, A052921.

Sequence in context: A247717 A128553 A190163 * A235612 A000340 A301880

Adjacent sequences:  A335548 A335549 A335550 * A335552 A335553 A335554

KEYWORD

nonn,easy

AUTHOR

Mauricio J. Santos, Sep 15 2020

EXTENSIONS

a(20)-a(29) from Alois P. Heinz, Sep 15 2020

STATUS

approved

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Last modified January 27 22:53 EST 2022. Contains 350654 sequences. (Running on oeis4.)