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A104566 Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product H*R of the infinite lower triangular matrices H = [1; 1,2; 1,2,1; 1 2,1,2; ...] and R = [1; 1,1; 1,1,1; 1,1,1,1; ...]. 2

%I

%S 1,3,2,4,3,1,6,5,3,2,7,6,4,3,1,9,8,6,5,3,2,10,9,7,6,4,3,1,12,11,9,8,6,

%T 5,3,2,13,12,10,9,7,6,4,3,1,15,14,12,11,9,8,6,5,3,2,16,15,13,12,10,9,

%U 7,6,4,3,1,18,17,15,14,12,11,9,8,6,5,3,2,19,18,16,15,13,12,10,9,7,6,4,3,1

%N Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product H*R of the infinite lower triangular matrices H = [1; 1,2; 1,2,1; 1 2,1,2; ...] and R = [1; 1,1; 1,1,1; 1,1,1,1; ...].

%F For 1 <= j <= i: T(i,j) = 3(i-j+1)/2 if i and j are of opposite parity; T(i,j) = 3(i-j)/2 + 1 if both i and j are odd; T(i,j) = 3(i-j)/2 + 2 if both i and j are even. - _Emeric Deutsch_, Mar 24 2005

%e The first few rows are

%e 1;

%e 3, 2;

%e 4, 3, 1;

%e 6, 5, 3, 2;

%e ...

%p T:=proc(i,j) if j>i then 0 elif i mod 2 = 1 and j mod 2 = 1 then 3*(i-j)/2+1 elif i mod 2 = 0 and j mod 2 = 0 then 3*(i-j)/2+2 elif i+j mod 2 = 1 then 3*(i-j+1)/2 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

%Y Row sums yield A001082.

%Y Columns 1, 3, 5, ... (starting at the diagonal entry) yield A032766.

%Y Columns 2, 4, 6, ... (starting at the diagonal entry) yield A045506.

%Y Row sums = 1, 5, 8, 16, 21, ... (generalized octagonal numbers, A001082). A006578(2n-1) = A001082(2n).

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Mar 15 2005

%E More terms from _Emeric Deutsch_, Mar 24 2005

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Last modified April 3 00:35 EDT 2020. Contains 333195 sequences. (Running on oeis4.)