|
%I #12 May 04 2021 02:02:25
%S 1,0,2,0,0,2,0,0,0,2,0,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,0,2,0,0,0,0,0,0,
%T 0,2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,2,0,0,
%U 0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,2
%N Triangle read by rows: (1, 2, 2, 2, ...) on the main diagonal and the rest zeros.
%H G. C. Greubel, <a href="/A136521/b136521.txt">Rows n = 0..25 of the triangle, flattened</a>
%F By columns, (1, 0, 0, 0, ...) in leftmost column; all others are (2, 0, 0, 0, ...).
%F By rows, row 1 = 1, others = (n-1) zeros followed by "2".
%F A007318(n,k) * T(n,k) = A124927(n,k).
%F T(n,k) * A007318(n,k) = A134058(n,k).
%F A001263(n,k) * T(n,k) = A136522(n,k).
%F From _G. C. Greubel_, May 03 2021: (Start)
%F T(n, k) = 2*[k=n] - [n=0].
%F Sum_{k=0..n} T(n, k) = A040000(n). (End)
%e First few rows of the triangle are:
%e 1;
%e 0, 2;
%e 0, 0, 2;
%e 0, 0, 0, 2;
%e 0, 0, 0, 0, 2;
%e ...
%t Table[2*Boole[k==n] -Boole[n==0], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, May 03 2021 *)
%o (Sage) flatten([[2*bool(k==n) -bool(n==0) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, May 03 2021
%Y Cf. A001263, A007318, A040000, A124927, A134058, A136522.
%K nonn,tabl,less,easy
%O 0,3
%A _Gary W. Adamson_, Jan 02 2008
%E More terms added by _G. C. Greubel_, May 03 2021
|
