cp's OEIS Frontend

A104570 Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product R*Q of the infinite lower triangular matrices R = [1; 1,1; 1,1,1; 1,1,1,1; ...] and Q = [1; 1,3; 1,3,1; 1,3,1,3; ...].

%I A104570 #17 Jul 24 2024 13:22:05
%S A104570 1,2,3,3,6,1,4,9,2,3,5,12,3,6,1,6,15,4,9,2,3,7,18,5,12,3,6,1,8,21,6,
%T A104570 15,4,9,2,3,9,24,7,18,5,12,3,6,1,10,27,8,21,6,15,4,9,2,3,11,30,9,24,7,
%U A104570 18,5,12,3,6,1,12,33,10,27,8,21,6,15,4,9,2,3,13,36,11,30,9,24,7,18,5,12,3,6,1
%N A104570 Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product R*Q of the infinite lower triangular matrices R = [1; 1,1; 1,1,1; 1,1,1,1; ...] and Q = [1; 1,3; 1,3,1; 1,3,1,3; ...].
%F A104570 Even columns (offset) = 1, 2, 3, ...; while odd columns = 3, 6, 9, ...
%F A104570 T(i,j) = i-j+1 if j <= i and j is odd; 3(i-j+1) if j <= i and j is even. - _Emeric Deutsch_, Mar 23 2005
%e A104570 First few rows of the triangle:
%e A104570   1;
%e A104570   2, 3;
%e A104570   3, 6, 1;
%e A104570   4, 9, 2, 3;
%e A104570   ...
%p A104570 T:=proc(i,j) if j>i then 0 elif j mod 2 = 1 then i-j+1 else 3*(i-j+1) fi end:for i from 1 to 14 do seq(T(i,j),j=1..i) od; # yields sequence in triangular form # _Emeric Deutsch_, Mar 23 2005
%t A104570 Q[i_, j_] := If[j <= i, 2 + (-1)^j, 0];
%t A104570 R[i_, j_] := If[j <= i, 1, 0];
%t A104570 T[i_, j_] := Sum[R[i, k]*Q[k, j], {k, 1, 13}];
%t A104570 Table[T[i, j], {i, 1, 13}, {j, 1, i}] // Flatten (* _Jean-François Alcover_, Jul 24 2024~ *)
%Y A104570 Cf. A035608, A074377, A104569.
%Y A104570 Row sums yield A035608. The product Q*R yields A104569.
%K A104570 nonn,tabl
%O A104570 1,2
%A A104570 _Gary W. Adamson_, Mar 16 2005
%E A104570 More terms from _Emeric Deutsch_, Mar 23 2005