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A174038 Triangle T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 3, read by rows. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
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
KEYWORD
nonn,tabl,less,easy
AUTHOR
Roger L. Bagula, Mar 06 2010
EXTENSIONS
Edited by G. C. Greubel, Apr 16 2021
STATUS
approved

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Last modified April 12 22:48 EDT 2024. Contains 371639 sequences. (Running on oeis4.)