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%I #8 May 07 2021 08:12:54
%S 1,1,1,1,1,1,1,2,2,1,1,2,3,2,1,1,2,5,4,2,1,1,2,6,10,6,2,1,1,2,9,18,14,
%T 6,2,1,1,2,7,23,35,23,7,2,1,1,2,9,34,63,51,21,6,1,1,1,1,7,30,84,126,
%U 84,30,7,1,1
%N Triangle T(n, k, q) = ceiling( binomial(n, k)*(1+q)/( (1+q)^2 + (k - floor(n/2))^2 ) ), with q = 1, read by rows.
%H G. C. Greubel, <a href="/A172281/b172281.txt">Rows n = 0..30 of the triangle, flattened</a>
%F T(n, k, q) = ceiling( binomial(n, k)*(1+q)/( (1+q)^2 + (k - floor(n/2))^2 ) ), with q = 1.
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 1, 2, 2, 1;
%e 1, 2, 3, 2, 1;
%e 1, 2, 5, 4, 2, 1;
%e 1, 2, 6, 10, 6, 2, 1;
%e 1, 2, 9, 18, 14, 6, 2, 1;
%e 1, 2, 7, 23, 35, 23, 7, 2, 1;
%e 1, 2, 9, 34, 63, 51, 21, 6, 1, 1;
%e 1, 1, 7, 30, 84, 126, 84, 30, 7, 1, 1;
%t T[n_, k_, q_]:= Ceiling[Binomial[n, k]*(q+1)/((1+q)^2 + (k - Floor[n/2])^2)];
%t Table[T[n, k, 1], {n, 0, 5}, {k, 0, n}]//Flatten (* modified by _G. C. Greubel_, May 07 2021 *)
%o (Sage)
%o def T(n,k,q): return ceil( binomial(n,k)*(1+q)/( (1+q)^2 + (k - n//2)^2 ) )
%o flatten([[T(n,k,1) for k in (0..n)] for n in (0..10)]) # _G. C. Greubel_, May 07 2021
%Y Cf. A172279 (q=0), this sequence (q=1).
%K nonn,tabl,less,easy
%O 0,8
%A _Roger L. Bagula_, Jan 30 2010
%E Edited by _G. C. Greubel_, May 07 2021
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