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

Author

R. J. Mathar, Dec 10 2015

Keywords

• nonn
• tabl
• easy

Examples

			  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
		

Crossrefs

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

Programs

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) ;

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)).