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A174032 Triangle, read by rows, T(n, k) = Sum_{j>=0} floor(binomial(n, k)/2^j). 1
1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 7, 10, 7, 1, 1, 8, 18, 18, 8, 1, 1, 10, 26, 38, 26, 10, 1, 1, 11, 39, 67, 67, 39, 11, 1, 1, 15, 53, 109, 137, 109, 53, 15, 1, 1, 16, 70, 165, 246, 246, 165, 70, 16, 1, 1, 18, 86, 236, 416, 498, 416, 236, 86, 18, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row Sums are: {1, 2, 5, 10, 26, 54, 112, 236, 493, 996, 2012, ...}.

LINKS

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

FORMULA

T(n, k) = Sum_{j>=0} floor(binomial(n, k)/2^j).

EXAMPLE

Triangle begins as:

  1;

  1,  1;

  1,  3,  1;

  1,  4,  4,   1;

  1,  7, 10,   7,   1;

  1,  8, 18,  18,   8,   1;

  1, 10, 26,  38,  26,  10,   1;

  1, 11, 39,  67,  67,  39,  11,   1;

  1, 15, 53, 109, 137, 109,  53,  15,  1;

  1, 16, 70, 165, 246, 246, 165,  70, 16,  1;

  1, 18, 86, 236, 416, 498, 416, 236, 86, 18, 1;

MATHEMATICA

T[n_, k_]:= Sum[Floor[Binomial[n, k]/2^j], {j, 0, infinity}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Nov 28 2019 *)

PROG

(PARI) T(n, k) = round(suminf(j=0, binomial(n, k)\2^j )); \\ G. C. Greubel, Nov 28 2019

CROSSREFS

Sequence in context: A026648 A026747 A026374 * A180979 A102716 A173076

Adjacent sequences:  A174029 A174030 A174031 * A174033 A174034 A174035

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Mar 06 2010

STATUS

approved

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Last modified July 11 23:53 EDT 2020. Contains 335654 sequences. (Running on oeis4.)