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%I #11 Apr 17 2021 02:13:08
%S 1,1,1,1,5,1,1,6,6,1,1,19,24,19,1,1,20,70,70,20,1,1,24,90,230,90,24,1,
%T 1,25,231,671,671,231,25,1,1,65,295,941,2083,941,295,65,1,1,66,684,
%U 2289,3024,3024,2289,684,66,1,1,70,750,3000,8580,9324,8580,3000,750,70,1
%N Triangle T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 3, read by rows.
%H G. C. Greubel, <a href="/A174038/b174038.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 = 3.
%e The triangle begins as:
%e 1;
%e 1, 1;
%e 1, 5, 1;
%e 1, 6, 6, 1;
%e 1, 19, 24, 19, 1;
%e 1, 20, 70, 70, 20, 1;
%e 1, 24, 90, 230, 90, 24, 1;
%e 1, 25, 231, 671, 671, 231, 25, 1;
%e 1, 65, 295, 941, 2083, 941, 295, 65, 1;
%e 1, 66, 684, 2289, 3024, 3024, 2289, 684, 66, 1;
%e 1, 70, 750, 3000, 8580, 9324, 8580, 3000, 750, 70, 1;
%t T[n_, k_, q_]:= Sum[q^j*Floor[Binomial[n, k]/2^j], {j, 0, 2*n}];
%t Table[T[n,k,3], {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,3): 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,3) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Apr 16 2021
%Y Cf. A174032 (q=1), A174037 (q=2), this sequence (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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