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
Examples
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;
...
Links
- Alois P. Heinz, Rows n = 1..141, flattened
Crossrefs
Programs
-
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 *)
Extensions
Edited and more terms from Alois P. Heinz, Oct 07 2009