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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.
0
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
3,1
LINKS
Miquel A. Fiol, E. Garriga, and J. L. A. Yebra, On twisted odd graphs, Combin. Probab. Comput. 9 (2000), 227-240.
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.
EXAMPLE
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
...
MATHEMATICA
T[n_, k_]:=If[k==1, n, If[1<k<=n, n+1-k, n-k]]; Flatten[Table[T[n, k], {n, 3, 9}, {k, 2n-1}]] (* Stefano Spezia, Aug 27 2024 *)
CROSSREFS
Cf. A001700.
Sequence in context: A250030 A316456 A370060 * A344893 A338946 A083716
KEYWORD
tabf,easy,sign
AUTHOR
Miquel A. Fiol, Aug 26 2024
STATUS
approved