A174037 - OEIS

%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