A078123 - OEIS

%I #13 Mar 06 2015 09:55:16

%S 1,2,1,5,6,1,23,51,18,1,239,861,477,54,1,5828,32856,25263,4347,162,1,

%T 342383,3013980,3016107,699813,39285,486,1,50110484,690729981,

%U 865184724,253656252,19053063,354051,1458,1,18757984046,406279238154

%N Square of infinite lower triangular matrix A078122.

%H Alois P. Heinz, <a href="/A078123/b078123.txt">Rows n = 0..60, flattened</a>

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

%e Square of A078122 = A078123 as can be seen by 4 X 4 submatrix:

%e [1,_0,_0,0]^2=[_1,_0,_0,_0]

%e [1,_1,_0,0]___[_2,_1,_0,_0]

%e [1,_3,_1,0]___[_5,_6,_1,_0]

%e [1,12,_9,1]___[23,51,18,_1]

%p S:= proc(i, j) option remember;

%p        add(M(i, k)*M(k, j), k=0..i)

%p     end:

%p M:= proc(i, j) option remember; `if`(j=0 or i=j, 1,

%p        add(S(i-1, k)*M(k, j-1), k=0..i-1))

%p     end:

%p seq(seq(S(n,k), k=0..n), n=0..10);  # _Alois P. Heinz_, Feb 27 2015

%t 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_ *)

%Y Cf. A078121, A078122, A078124, A078125.

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Nov 18 2002