A091453 Triangular array T(n,k) read by rows in which row n consists of the numbers floor(2n/k), k=1,2,...,2n+1.

0, 0, 2, 1, 0, 4, 2, 1, 1, 0, 6, 3, 2, 1, 1, 1, 0, 8, 4, 2, 2, 1, 1, 1, 1, 0, 10, 5, 3, 2, 2, 1, 1, 1, 1, 1, 0, 12, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 14, 7, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 16, 8, 5, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 18, 9, 6, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 20, 10, 6

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..10201

Formula

a(n) = floor(1/(sqrt(n)-floor(sqrt(n)))) for n not a square; a(n) = 0 otherwise. - Andrew Howroyd, Oct 02 2019

Example

First five rows:
  0
  0 2 1
  0 4 2 1 1
  0 6 3 2 1 1 1
  0 8 4 2 2 1 1 1 1

Prog

(PARI) T(n, k) = 2*n\k;
tabf(nn) = for (n=0, nn, for (k=1, 2*n+1, print1(T(n, k), ", ")); print()); \\ Michel Marcus, Sep 30 2016
(PARI) a(n)={if(n<1, 0, my(t=sqrtint(n-1)); 2*t\(n-t^2))} \\ Andrew Howroyd, Oct 02 2019

Crossrefs

Cf. A013942 (without first column).

Cf. A091449, A327898.

Sequence in context: A293808 A327805 A276689 * A062173 A004558 A129699

Adjacent sequences: A091450 A091451 A091452 * A091454 A091455 A091456

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 03 2004

Extensions

Offset corrected and missing a(99) inserted by Andrew Howroyd, Oct 02 2019

Status

approved