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

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 A093682

Adjacent sequences: A265621 A265622 A265623 * A265625 A265626 A265627

Keyword

nonn,tabl,easy

Author

R. J. Mathar, Dec 10 2015

Status

approved