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A228273 T(n,k) is the number of s in {1,...,n}^n having longest ending contiguous subsequence with the same value of length k; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 7
1, 0, 1, 0, 2, 2, 0, 18, 6, 3, 0, 192, 48, 12, 4, 0, 2500, 500, 100, 20, 5, 0, 38880, 6480, 1080, 180, 30, 6, 0, 705894, 100842, 14406, 2058, 294, 42, 7, 0, 14680064, 1835008, 229376, 28672, 3584, 448, 56, 8, 0, 344373768, 38263752, 4251528, 472392, 52488, 5832, 648, 72, 9 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

FORMULA

T(0,0) = 1, else T(n,k) = 0 for k<1 or k>n, else T(n,n) = n, else T(n,k) = (n-1)*n^(n-k).

Sum_{k=0..n}   T(n,k) = A000312(n).

Sum_{k=0..n} k*T(n,k) = A031972(n).

EXAMPLE

T(0,0) = 1: [].

T(1,1) = 1: [1].

T(2,1) = 2: [1,2], [2,1].

T(2,2) = 2: [1,1], [2,2].

T(3,1) = 18: [1,1,2], [1,1,3], [1,2,1], [1,2,3], [1,3,1], [1,3,2], [2,1,2], [2,1,3], [2,2,1], [2,2,3], [2,3,1], [2,3,2], [3,1,2], [3,1,3], [3,2,1], [3,2,3], [3,3,1], [3,3,2].

T(3,2) = 6: [1,2,2], [1,3,3], [2,1,1], [2,3,3], [3,1,1], [3,2,2].

T(3,3) = 3: [1,1,1], [2,2,2], [3,3,3].

Triangle T(n,k) begins:

  1;

  0,        1;

  0,        2,       2;

  0,       18,       6,      3;

  0,      192,      48,     12,     4;

  0,     2500,     500,    100,    20,    5;

  0,    38880,    6480,   1080,   180,   30,   6;

  0,   705894,  100842,  14406,  2058,  294,  42,  7;

  0, 14680064, 1835008, 229376, 28672, 3584, 448, 56,  8;

MAPLE

T:= (n, k)-> `if`(n=0 and k=0, 1, `if`(k<1 or k>n, 0,

             `if`(k=n, n, (n-1)*n^(n-k)))):

seq(seq(T(n, k), k=0..n), n=0..12);

MATHEMATICA

f[0, 0]=1;

f[n_, k_]:=Which[1<=k<=n-1, n^(n-k)*(n-1), k<1, 0, k==n, n, k>n, 0];

Table[Table[f[n, k], {k, 0, n}], {n, 0, 10}]//Grid (* Geoffrey Critzer, May 19 2014 *)

CROSSREFS

Row sums give: A000312.

Columns k=0-4 give: A000007, A066274(n) = 2*A081131(n) for n>1, A053506(n) for n>2, A055865(n-1) = A085389(n-1) for n>3, A085390(n-1) for n>4.

Main diagonal gives: A028310.

Lower diagonals include (offsets may differ): A002378, A045991, A085537, A085538, A085539.

Cf. A228154, A228617.

Sequence in context: A091466 A134085 A151339 * A069521 A245687 A228617

Adjacent sequences:  A228270 A228271 A228272 * A228274 A228275 A228276

KEYWORD

nonn,tabl,easy

AUTHOR

Alois P. Heinz, Aug 19 2013

STATUS

approved

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Last modified January 18 07:55 EST 2022. Contains 350454 sequences. (Running on oeis4.)