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

1,3

Links

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

Formula

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

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

Example

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;

Mathematica

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

Prog

(Magma)
A278112:=func<n, k|Isqrt(2*n^2 div k)>;
[[A278112(n, k):k in[1..2*n^2]]:n in[1..5]];

Crossrefs

Cf. A277647.

Sequence in context: A194606 A331180 A126389 * A286132 A105551 A305195

Adjacent sequences: A278109 A278110 A278111 * A278113 A278114 A278115

Keyword

nonn,tabf,easy

Author

Jason Kimberley, Feb 09 2017

Status

approved