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%I #15 Feb 26 2024 17:05:34
%S 1,1,1,1,0,1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,1,0,1,
%T 0,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,
%U 0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1
%N Triangle read by rows: starting with A138174, replace left border with (1, 1, 1, ...).
%C Row sums = (1, 2, 2, 3, 3, 4, 4, 5, 5, ...).
%H G. C. Greubel, <a href="/A135839/b135839.txt">Table of n, a(n) for the first 50 rows</a>
%F Given A128174, replace left border with (1, 1, 1, ...). Triangle read by rows, odd rows = n terms of (1, 0, 1, ...); even rows = n terms of (1, 1, 0, 1, 0, 1, ...). By columns, leftmost column = (1, 1, 1, ...); all others = (1, 0, 1, 0, 1, ...).
%F T(n,1) = T(n,n) = 1, T(n,k) = (1 - (-1)^(n-k-1))/2. - _G. C. Greubel_,Dec 05 2016
%e First few rows of the triangle are:
%e 1;
%e 1, 1;
%e 1, 0, 1;
%e 1, 1, 0, 1;
%e 1, 0, 1, 0, 1;
%e 1, 1, 0, 1, 0, 1;
%e 1, 0, 1, 0, 1, 0, 1;
%e ...
%t T[1, 1] := 1; T[n_, 1] := 1; T[n_, n_] := 1; T[n_, k_] := (1 - (-1)^(n - k + 1))/2; Table[T[n, k], {n, 1, 10}, {k, 1, n}]//Flatten (* _G. C. Greubel_, Dec 05 2016 *)
%t Flatten[Table[Join[{1},PadLeft[{},n,{0,1}]],{n,0,20}]] (* _Harvey P. Dale_, Feb 26 2024 *)
%K nonn,tabl
%O 1,1
%A _Gary W. Adamson_, Dec 01 2007
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