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A174105
Triangle T(n, k) = Sum_{j=0..10} (-1)^j * floor(binomial(n, k)/2^(n-j)), read by rows.
1
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, ...
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
KEYWORD
nonn,tabl,easy,less
AUTHOR
Roger L. Bagula, Mar 07 2010
EXTENSIONS
Edited by G. C. Greubel, Feb 10 2021
STATUS
approved