A172281 - OEIS

%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