A096044 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^10-M)/9, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

1, 11, 2, 111, 33, 3, 1111, 444, 66, 4, 11111, 5555, 1110, 110, 5, 111111, 66666, 16665, 2220, 165, 6, 1111111, 777777, 233331, 38885, 3885, 231, 7, 11111111, 8888888, 3111108, 622216, 77770, 6216, 308, 8, 111111111, 99999999, 39999996, 9333324, 1399986, 139986, 9324, 396, 9

Offset

1,2

Links

Alois P. Heinz, Rows n = 1..141, flattened

Example

Triangle T(n,k) begins:
       1;
      11,     2;
     111,    33,     3;
    1111,   444,    66,    4;
   11111,  5555,  1110,  110,   5;
  111111, 66666, 16665, 2220, 165, 6;
  ...

Maple

P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^10-M)/9 end: T:= (n, k)-> P(n+1)[n+1, k]: seq(seq(T(n, k), k=1..n), n=1..11);  # Alois P. Heinz, Oct 07 2009

Mathematica

P[n_] := P[n] = With[{M = Array[Binomial[#1-1, #2-1]&, {n, n}]}, (MatrixPower[M, 10] - M)/9]; T[n_, k_] := P[n+1][[n+1, k]]; Table[ Table[T[n, k], {k, 1, n}], {n, 1, 11}] // Flatten (* Jean-François Alcover, Jan 28 2015, after Alois P. Heinz *)

Crossrefs

Cf. A007318. First column gives A000042. Row sums give A016135.

Cf. A096034, A096035, A096039, A096040, A096041, A096042, A096043.

Sequence in context: A110767 A089365 A130217 * A160464 A038316 A139311

Adjacent sequences: A096041 A096042 A096043 * A096045 A096046 A096047

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 17 2004

Extensions

Edited and more terms from Alois P. Heinz, Oct 07 2009

Status

approved