login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
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: A245471 A258090 A112157 * A093682 A187883 A134543

Adjacent sequences:  A265621 A265622 A265623 * A265625 A265626 A265627

KEYWORD

nonn,tabl,easy

AUTHOR

R. J. Mathar, Dec 10 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 06:03 EST 2019. Contains 329310 sequences. (Running on oeis4.)