A174557 Triangle T(n, k) = -floor(n/k) with T(n, n) = 1, read by rows.

1, -2, 1, -3, -1, 1, -4, -2, -1, 1, -5, -2, -1, -1, 1, -6, -3, -2, -1, -1, 1, -7, -3, -2, -1, -1, -1, 1, -8, -4, -2, -2, -1, -1, -1, 1, -9, -4, -3, -2, -1, -1, -1, -1, 1, -10, -5, -3, -2, -2, -1, -1, -1, -1, 1, -11, -5, -3, -2, -2, -1, -1, -1, -1, -1, 1, -12, -6, -4, -3, -2, -2, -1, -1, -1, -1, -1, 1

Offset

1,2

Links

G. C. Greubel, Rows n = 1..30 of the triangle, flattened

Formula

T(n, k) = A010766(n, k)*A154990(n, k).

T(n, k) = -floor(n/k) with T(n, n) = 1. - G. C. Greubel, Mar 06 2021

Example

Table begins:
    1;
   -2,  1;
   -3, -1,  1;
   -4, -2, -1,  1;
   -5, -2, -1, -1,  1;
   -6, -3, -2, -1, -1,  1;
   -7, -3, -2, -1, -1, -1,  1;
   -8, -4, -2, -2, -1, -1, -1,  1;
   -9, -4, -3, -2, -1, -1, -1, -1,  1;
  -10, -5, -3, -2, -2, -1, -1, -1, -1, 1;

Mathematica

Table[If[k==n, 1, -Floor[n/k]], {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Mar 06 2021 *)

Prog

(Sage) flatten([[1 if k==n else -(n//k) for k in [1..n]] for n in [1..12]]) # G. C. Greubel, Mar 06 2021
(Magma) [k eq n select 1 else -Floor(n/k): k in [1..n], n in [1..12]]; // G. C. Greubel, Mar 06 2021

Crossrefs

Cf. A010766, A154990.

Sequence in context: A182715 A088425 A141294 * A010766 A135841 A210992

Adjacent sequences: A174554 A174555 A174556 * A174558 A174559 A174560

Keyword

sign,tabl

Author

Mats Granvik, Paul D. Hanna, Mar 22 2010

Status

approved