OFFSET
0,5
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 2.
EXAMPLE
Triangle begins as:
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;
1, 17, 93, 197, 197, 93, 17, 1;
1, 32, 124, 304, 464, 304, 124, 32, 1;
1, 33, 204, 540, 768, 768, 540, 204, 33, 1;
1, 36, 237, 752, 1556, 1788, 1556, 752, 237, 36, 1;
MATHEMATICA
T[n_, k_, q_]:= Sum[q^j*Floor[Binomial[n, k]/2^j], {j, 0, 2*n}];
Table[T[n, k, 2], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 16 2021 *)
PROG
(Magma)
T:= func< n, k, q | (&+[q^j*Floor(Binomial(n, k)/2^j): j in [0..2*n]]) >;
[T(n, k, 2): k in [0..n], n in [0..12]]; // G. C. Greubel, Apr 16 2021
(Sage)
def T(n, k, q): return sum(q^j*( binomial(n, k)//2^j ) for j in (0..2*n))
flatten([[T(n, k, 2) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 16 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Mar 06 2010
EXTENSIONS
Edited by G. C. Greubel, Apr 16 2021
STATUS
approved