A174105 Triangle T(n, k) = Sum_{j=0..10} (-1)^j * floor(binomial(n, k)/2^(n-j)), read by rows.

683, 341, 341, 171, 341, 171, 85, 256, 256, 85, 43, 171, 256, 171, 43, 21, 106, 214, 214, 106, 21, 11, 64, 160, 214, 160, 64, 11, 5, 37, 111, 187, 187, 111, 37, 5, 3, 21, 75, 149, 187, 149, 75, 21, 3, 1, 12, 48, 111, 168, 168, 111, 48, 12, 1, 1, 6, 30, 80, 140, 168, 140, 80, 30, 6, 1

Offset

0,1

Comments

Row sums are: 683, 682, 683, 682, 684, 682, 684, 680, 683, 680, 682, ...

Links

G. C. Greubel, Rows n = 0..100 of the triangle, flattened

Formula

T(n, k) = Sum_{j=0..10} (-1)^j * floor(binomial(n, k)/2^(n-j)).

Example

Triangle begins as:
  683;
  341, 341;
  171, 341, 171;
   85, 256, 256,  85;
   43, 171, 256, 171,  43;
   21, 106, 214, 214, 106,  21;
   11,  64, 160, 214, 160,  64,  11;
    5,  37, 111, 187, 187, 111,  37,  5;
    3,  21,  75, 149, 187, 149,  75, 21,  3;
    1,  12,  48, 111, 168, 168, 111, 48, 12, 1;
    1,   6,  30,  80, 140, 168, 140, 80, 30, 6, 1;

Mathematica

T[n_, k_]:= Sum[(-1)^j*Floor[Binomial[n, k]/2^(n-j)], {j, 0, 10}];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten

Prog

(Sage)
def A174105(n, k): return sum( (-1)^j*floor(binomial(n, k)/2^(n-j)) for j in (0..10) )
flatten([[A174105(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 10 2021
(Magma)
A174105:= func< n, k | (&+[(-1)^j*Floor(Binomial(n, k)/2^(n-j)): j in [0..10]]) >;
[A174105(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 10 2021

Crossrefs

Sequence in context: A327417 A145321 A175155 * A320772 A045154 A300193

Adjacent sequences: A174102 A174103 A174104 * A174106 A174107 A174108

Keyword

nonn,tabl,easy,less

Author

Roger L. Bagula, Mar 07 2010

Extensions

Edited by G. C. Greubel, Feb 10 2021

Status

approved