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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A256311 Number T(n,k) of length 3n words such that all letters of the k-ary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting triples of identical letters into the initially empty word; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 15
1, 0, 1, 0, 1, 3, 0, 1, 18, 12, 0, 1, 97, 198, 55, 0, 1, 530, 2520, 1820, 273, 0, 1, 2973, 29886, 42228, 15300, 1428, 0, 1, 17059, 347907, 859180, 564585, 122094, 7752, 0, 1, 99657, 4048966, 16482191, 17493938, 6577494, 942172, 43263 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Rows n = 0..140, flattened

FORMULA

T(n,k) = Sum_{i=0..k} (-1)^i * A213028(n,k-i) / (i!*(k-i)!).

EXAMPLE

T(0,0) = 1: (the empty word).

T(1,1) = 1: aaa.

T(2,1) = 1: aaaaaa.

T(2,2) = 3: aaabbb, aabbba, abbbaa.

T(3,1) = 1: aaaaaaaaa.

T(3,2) = 18: aaaaaabbb, aaaaabbba, aaaabbbaa, aaabaaabb, aaabbaaab, aaabbbaaa, aaabbbbbb, aabaaabba, aabbaaaba, aabbbaaaa, aabbbabbb, aabbbbbba, abaaabbaa, abbaaabaa, abbbaaaaa, abbbaabbb, abbbabbba, abbbbbbaa.

T(3,3) = 12: aaabbbccc, aaabbcccb, aaabcccbb, aabbbaccc, aabbbccca, aabbcccba, aabcccbba, abbbaaccc, abbbaccca, abbbcccaa, abbcccbaa, abcccbbaa.

Triangle T(n,k) begins:

  1;

  0, 1;

  0, 1,     3;

  0, 1,    18,     12;

  0, 1,    97,    198,     55;

  0, 1,   530,   2520,   1820,    273;

  0, 1,  2973,  29886,  42228,  15300,   1428;

  0, 1, 17059, 347907, 859180, 564585, 122094, 7752;

MAPLE

A:= (n, k)-> `if`(n=0, 1,

    k/n *add(binomial(3*n, j) *(n-j) *(k-1)^j, j=0..n-1)):

T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k):

seq(seq(T(n, k), k=0..n), n=0..10);

CROSSREFS

Columns k=0-10 give: A000007, A057427, A321032, A321033, A321034, A321035, A321036, A321037, A321038, A321039, A321040.

Row sums give A321031.

Main diagonal gives A001764.

T(2n,n) gives A321041.

Cf. A256117, A213028.

Sequence in context: A279031 A304336 A287315 * A022695 A278325 A226780

Adjacent sequences:  A256308 A256309 A256310 * A256312 A256313 A256314

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Mar 25 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 January 21 13:44 EST 2019. Contains 319350 sequences. (Running on oeis4.)