A174038 Triangle T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 3, read by rows.

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, 1, 25, 231, 671, 671, 231, 25, 1, 1, 65, 295, 941, 2083, 941, 295, 65, 1, 1, 66, 684, 2289, 3024, 3024, 2289, 684, 66, 1, 1, 70, 750, 3000, 8580, 9324, 8580, 3000, 750, 70, 1

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 = 3.

Example

The triangle begins as:
  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;
  1, 25, 231,  671,  671,  231,   25,    1;
  1, 65, 295,  941, 2083,  941,  295,   65,   1;
  1, 66, 684, 2289, 3024, 3024, 2289,  684,  66,  1;
  1, 70, 750, 3000, 8580, 9324, 8580, 3000, 750, 70, 1;

Mathematica

T[n_, k_, q_]:= Sum[q^j*Floor[Binomial[n, k]/2^j], {j, 0, 2*n}];
Table[T[n, k, 3], {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, 3): 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, 3) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 16 2021

Crossrefs

Cf. A174032 (q=1), A174037 (q=2), this sequence (q=3).

Sequence in context: A297986 A298635 A171146 * A328098 A200401 A214228

Adjacent sequences: A174035 A174036 A174037 * A174039 A174040 A174041

Keyword

nonn,tabl,less,easy

Author

Roger L. Bagula, Mar 06 2010

Extensions

Edited by G. C. Greubel, Apr 16 2021

Status

approved