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A104567 Triangle read by rows: T(i,j) = i-j+1 if j is odd; T(i,j) = 2(i-j+1) if j is even (1 <= j <= i).

%I A104567 #13 Sep 03 2018 17:07:13
%S A104567 1,2,2,3,4,1,4,6,2,2,5,8,3,4,1,6,10,4,6,2,2,7,12,5,8,3,4,1,8,14,6,10,
%T A104567 4,6,2,2,9,16,7,12,5,8,3,4,1,10,18,8,14,6,10,4,6,2,2,11,20,9,16,7,12,
%U A104567 5,8,3,4,1,12,22,10,18,8,14,6,10,4,6,2,2,13,24,11,20,9,16,7,12,5,8,3,4,1,14
%N A104567 Triangle read by rows: T(i,j) = i-j+1 if j is odd; T(i,j) = 2(i-j+1) if j is even (1 <= j <= i).
%C A104567 T(i,j) is the (i,j)-entry (1<=j<=i) of the product R*H of the infinite lower triangular matrices R = [1; 1,1; 1,1,1; 1,1,1,1; ...] and H = [1; 1,2; 1,2,1; 1 2,1,2; ...]. Row sums yield A006578. H*R yields A104566. - _Emeric Deutsch_, Mar 24 2005
%H A104567 Harvey P. Dale, <a href="/A104567/b104567.txt">Table of n, a(n) for n = 1..1000</a>
%F A104567 T(i,j) = i-j+1 if j is odd; T(i,j) = 2(i-j+1) if j is even (1 <= j <= i). - _Emeric Deutsch_, Mar 24 2005
%e A104567 The first few rows are:
%e A104567   1;
%e A104567   2, 2;
%e A104567   3, 4, 1;
%e A104567   4, 6, 2, 2;
%p A104567 T:=proc(i,j) if j>i then 0 elif j mod 2 = 1 then i-j+1 elif j mod 2 = 0 then 2*(i-j+1) else 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 24 2005
%t A104567 Table[If[OddQ[j],i-j+1,2(i-j+1)],{i,20},{j,i}]//Flatten (* _Harvey P. Dale_, Sep 03 2018 *)
%Y A104567 Cf. A001082, A006578, A104566, A104568.
%Y A104567 Cf. A006578, A104566.
%K A104567 nonn,tabl
%O A104567 1,2
%A A104567 _Gary W. Adamson_, Mar 16 2005
%E A104567 More terms from _Emeric Deutsch_, Mar 24 2005