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A278112
Triangle T(n,k) = floor(n sqrt(2/k)) for 1 <= k <= 2n^2, read by rows.
5
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
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
KEYWORD
nonn,tabf,easy
AUTHOR
Jason Kimberley, Feb 09 2017
STATUS
approved