A393017 Triangle read by rows: T(n, k) = denominator(8*n^3*k/(k^2+4*n^2)).

5, 17, 5, 37, 5, 5, 65, 17, 73, 5, 101, 13, 109, 29, 1, 145, 37, 17, 5, 169, 5, 197, 25, 205, 53, 221, 29, 5, 257, 65, 265, 17, 281, 73, 305, 5, 325, 41, 37, 85, 349, 5, 373, 97, 5, 401, 101, 409, 13, 17, 109, 449, 29, 481, 1, 485, 61, 493, 125, 509, 65, 533, 137, 565, 73, 5

Offset

1,1

Comments

Denominators of the rational numbers 8*n^3*k/(k^2+4*n^2) for 1 <= k <= n, related to the Witch of Agnesi curve.

All terms are odd.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3240

Wikipedia, Witch of Agnesi.

Example

Triangle begins:
  5;
  17, 5;
  37, 5, 5;
  65, 17, 73, 5;
  101, 13, 109, 29, 1;
  145, 37, 17, 5, 169, 5;
  197, 25, 205, 53, 221, 29, 5;
  257, 65, 265, 17, 281, 73, 305, 5;
  325, 41, 37, 85, 349, 5, 373, 97, 5;

Mathematica

T[n_, k_]:=Denominator[8*n^3*k/(k^2+4*n^2)]; Tri[nmax_]:=Table[T[n, k], {n, 1, nmax}, {k, 1, n}];
nmax=10; Flatten[Tri[nmax]]

Prog

(Magma) T := function(n, k) return Denominator(8*n^3*k/(k^2 + 4*n^2)); end function;
Triangle := function(nmax) return [ [ T(n, k) : k in [1..n] ] : n in [1..nmax] ];
end function; nmax := 10; Triangle(nmax); &cat Triangle(nmax);

Crossrefs

Cf. A393016

Cf. A053755 (column 1), A228564 (column 2).

Sequence in context: A340706 A093558 A170866 * A337031 A125636 A355658

Adjacent sequences: A393014 A393015 A393016 * A393018 A393019 A393020

Keyword

nonn,tabl,frac

Author

Vincenzo Librandi, Feb 10 2026

Status

approved