A078123 Square of infinite lower triangular matrix A078122.

1, 2, 1, 5, 6, 1, 23, 51, 18, 1, 239, 861, 477, 54, 1, 5828, 32856, 25263, 4347, 162, 1, 342383, 3013980, 3016107, 699813, 39285, 486, 1, 50110484, 690729981, 865184724, 253656252, 19053063, 354051, 1458, 1, 18757984046, 406279238154

Offset: 0

Author

Paul D. Hanna, Nov 18 2002

Keywords

• nonn
• tabl

Examples

			Square of A078122 = A078123 as can be seen by 4 X 4 submatrix:
[1,_0,_0,0]^2=[_1,_0,_0,_0]
[1,_1,_0,0]___[_2,_1,_0,_0]
[1,_3,_1,0]___[_5,_6,_1,_0]
[1,12,_9,1]___[23,51,18,_1]
		

Links

• Alois P. Heinz, Rows n = 0..60, flattened

Crossrefs

Cf. A078121, A078122, A078124, A078125.

Programs

Maple

S:= proc(i, j) option remember;
       add(M(i, k)*M(k, j), k=0..i)
    end:
M:= proc(i, j) option remember; `if`(j=0 or i=j, 1,
       add(S(i-1, k)*M(k, j-1), k=0..i-1))
    end:
seq(seq(S(n,k), k=0..n), n=0..10);  # Alois P. Heinz, Feb 27 2015

Mathematica

S[i_, j_] := S[i, j] = Sum[M[i, k]*M[k, j], {k, 0, i}]; M[i_, j_] := M[i, j] = If[j == 0 || i == j, 1, Sum[S[i-1, k]*M[k, j-1], {k, 0, i-1}]]; Table[Table[S[n, k], {k, 0, n}], {n, 0, 10}] // Flatten (* Jean-François Alcover, Mar 06 2015, after Alois P. Heinz *)

Formula

M(1, j) = A078125(j), M(j+1, j)=2*3^j.