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A265624 revision #12

A265624

Array T(n,k): The number of words of length n in an alphabet of size k which do not contain 4 consecutive letters.

1, 1, 2, 1, 4, 3, 0, 8, 9, 4, 0, 14, 27, 16, 5, 0, 26, 78, 64, 25, 6, 0, 48, 228, 252, 125, 36, 7, 0, 88, 666, 996, 620, 216, 49, 8, 0, 162, 1944, 3936, 3080, 1290, 343, 64, 9, 0, 298, 5676, 15552, 15300, 7710, 2394, 512, 81, 10, 0, 548, 16572, 61452

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..59.

FORMULA

T(2,k) = k^2.

T(3,k) = k^3.

T(4,k) = k*(k+1)*(k^2+3*k+3).

T(5,k) = k*(k+1)*(k^3+4*k^2+6*k+2).

T(6,k) = k*(k+1)^2*(k^3+4*k^2+6*k+1).

G.f. of row k: k*x*(1+x+x^2)/(1+(1-k)*x*(x^2+x+1)).

EXAMPLE

1 2 3 4 5 6 7 8

1 4 9 16 25 36 49 64

1 8 27 64 125 216 343 512

0 14 78 252 620 1290 2394 4088

0 26 228 996 3080 7710 16716 32648

0 48 666 3936 15300 46080 116718 260736

0 88 1944 15552 76000 275400 814968 2082304

0 162 5676 61452 377520 1645950 5690412 16629816

MAPLE

A265624 := proc(n, k)

local x;

k*x*(1+x+x^2)/(1+(1-k)*x*(x^2+x+1)) ;

coeftayl(%, x=0, n) ;

end proc;

seq(seq(A265624(d-k, k), k=1..d-1), d=2..10) ;

CROSSREFS

Cf. A135491 (column k=2), A181137 (k=3), A188714 (k=4), A265583 (not 2 consecutive letters), A265584 (not 3 consecutive letters).

Sequence in context: A352548 A258090 A112157 * A332332 A335259 A378037

Adjacent sequences: A265621 A265622 A265623 * A265625 A265626 A265627

KEYWORD

nonn,tabl,easy

AUTHOR

R. J. Mathar, Dec 10 2015

STATUS

reviewed