A278112 Triangle T(n,k) = floor(n sqrt(2/k)) for 1 <= k <= 2n^2, read by rows.

1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 5, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Jason Kimberley, Feb 09 2017

Keywords

• nonn
• tabf
• easy

Examples

			The first five rows are:
1, 1;
2, 2, 1, 1, 1, 1, 1, 1;
4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
5, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
7, 5, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
		

Links

• Jason Kimberley, Table of n, a(n) for n = 1..11050 (rows 1..25, flattened)

Crossrefs

Cf. A277647.

Programs

Magma

A278112:=func;
[[A278112(n,k):k in[1..2*n^2]]:n in[1..5]];

Mathematica

Table[Floor[n Sqrt[2/k]], {n, 5}, {k, 2 n^2}] // Flatten (* Michael De Vlieger, Feb 17 2017 *)

Formula

T(n,k) = A000196(A278111(n)).

T(n,k)sqrt(k) <= n sqrt(2) < (T(n,k)+1)sqrt(k).