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%I #13 Apr 17 2021 02:14:13
%S 1,1,1,1,4,1,1,5,5,1,1,12,16,12,1,1,13,36,36,13,1,1,16,49,92,49,16,1,
%T 1,17,93,197,197,93,17,1,1,32,124,304,464,304,124,32,1,1,33,204,540,
%U 768,768,540,204,33,1,1,36,237,752,1556,1788,1556,752,237,36,1
%N Triangle T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 2, read by rows.
%H G. C. Greubel, <a href="/A174037/b174037.txt">Rows n = 0..50 of the triangle, flattened</a>
%F T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 2.
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 4, 1;
%e 1, 5, 5, 1;
%e 1, 12, 16, 12, 1;
%e 1, 13, 36, 36, 13, 1;
%e 1, 16, 49, 92, 49, 16, 1;
%e 1, 17, 93, 197, 197, 93, 17, 1;
%e 1, 32, 124, 304, 464, 304, 124, 32, 1;
%e 1, 33, 204, 540, 768, 768, 540, 204, 33, 1;
%e 1, 36, 237, 752, 1556, 1788, 1556, 752, 237, 36, 1;
%t T[n_, k_, q_]:= Sum[q^j*Floor[Binomial[n, k]/2^j], {j,0,2*n}];
%t Table[T[n,k,2], {n,0,12}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Apr 16 2021 *)
%o (Magma)
%o T:= func< n,k,q | (&+[q^j*Floor(Binomial(n,k)/2^j): j in [0..2*n]]) >;
%o [T(n,k,2): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Apr 16 2021
%o (Sage)
%o def T(n,k,q): return sum(q^j*( binomial(n,k)//2^j ) for j in (0..2*n))
%o flatten([[T(n,k,2) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Apr 16 2021
%Y Cf. A174032 (q=1), this sequence (q=2), A174038 (q=3).
%K nonn,tabl,less,easy
%O 0,5
%A _Roger L. Bagula_, Mar 06 2010
%E Edited by _G. C. Greubel_, Apr 16 2021
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