login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Triangular array T(n,k) read by rows in which row n consists of the numbers floor(2n/k), k=1,2,...,2n+1.
8

%I #15 Oct 02 2019 11:26:39

%S 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,

%T 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,

%U 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

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

%H Andrew Howroyd, <a href="/A091453/b091453.txt">Table of n, a(n) for n = 0..10201</a>

%F a(n) = floor(1/(sqrt(n)-floor(sqrt(n)))) for n not a square; a(n) = 0 otherwise. - _Andrew Howroyd_, Oct 02 2019

%e First five rows:

%e 0

%e 0 2 1

%e 0 4 2 1 1

%e 0 6 3 2 1 1 1

%e 0 8 4 2 2 1 1 1 1

%o (PARI) T(n, k) = 2*n\k;

%o tabf(nn) = for (n=0, nn, for (k=1, 2*n+1, print1(T(n,k), ", ")); print()); \\ _Michel Marcus_, Sep 30 2016

%o (PARI) a(n)={if(n<1, 0, my(t=sqrtint(n-1)); 2*t\(n-t^2))} \\ _Andrew Howroyd_, Oct 02 2019

%Y Cf. A013942 (without first column).

%Y Cf. A091449, A327898.

%K nonn,tabf

%O 0,3

%A _Clark Kimberling_, Feb 03 2004

%E Offset corrected and missing a(99) inserted by _Andrew Howroyd_, Oct 02 2019