A375747 Table read by rows: T(n,k) for n >= 3 and k=1,2,...,2*n-1 are the distinct eigenvalues of the twisted odd graph O^(sigma)_n.

3, 2, 1, -1, -2, 4, 3, 2, 1, -1, -2, -3, 5, 4, 3, 2, 1, -1, -2, -3, -4, 6, 5, 4, 3, 2, 1, -1, -2, -3, -4, -5, 7, 6, 5, 4, 3, 2, 1, -1, -2, -3, -4, -5, -6, 8, 7, 6, 5, 4, 3, 2, 1, -1, -2, -3, -4, -5, -6, -7, 9, 8, 7, 6, 5, 4, 3, 2, 1, -1, -2, -3, -4, -5, -6, -7, -8

Offset: 3

Author

Miquel A. Fiol, Aug 26 2024

Keywords

• tabf
• easy
• sign

Examples

			The table begins:
  3  2  1 -1 -2
  4  3  2  1 -1 -2 -3
  5  4  3  2  1 -1 -2 -3 -4
  6  5  4  3  2  1 -1 -2 -3 -4 -5
  7  6  5  4  3  2  1 -1 -2 -3 -4 -5 -6
  ...
		

Links

• Miquel A. Fiol, E. Garriga, and J. L. A. Yebra, On twisted odd graphs, Combin. Probab. Comput. 9 (2000), 227-240.

Crossrefs

Cf. A001700.

Programs

Mathematica

T[n_,k_]:=If[k==1, n, If[1Stefano Spezia, Aug 27 2024 *)

Formula

T(n,1) = n; T(n,k) = n+1-k for k=2,...,n; T(n,k) = n-k for k=n+1,...,2n-1.