login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A174037 Triangle T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 2, read by rows. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

Cf. A174032 (q=1), this sequence (q=2), A174038 (q=3).

Sequence in context: A136489 A166455 A171142 * A173077 A131239 A114033

Adjacent sequences:  A174034 A174035 A174036 * A174038 A174039 A174040

KEYWORD

nonn,tabl,less,easy

AUTHOR

Roger L. Bagula, Mar 06 2010

EXTENSIONS

Edited by G. C. Greubel, Apr 16 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)