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

0,2

Links

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

Formula

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

Example

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]

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 *)

Crossrefs

Cf. A078121, A078122, A078124, A078125.

Sequence in context: A178121 A302595 A113345 * A342968 A323312 A231774

Adjacent sequences: A078120 A078121 A078122 * A078124 A078125 A078126

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 18 2002

Status

approved