A060408 Triangle T(n,k) in which n-th row gives numbers of super edge-magic labelings of (n,k)-graphs, for n >= 2, and 1 <= k <= 2n-3.

1, 3, 2, 1, 6, 6, 6, 4, 2, 10, 14, 20, 24, 24, 16, 8, 15, 26, 48, 80, 120, 144, 144, 96, 48, 21, 44, 99, 212, 420, 720, 1080, 1296, 1296, 864, 432, 28, 68, 180, 464, 1140, 2520, 5040, 8640, 12960, 15552, 15552, 10368, 5184

Offset: 2

Author

N. J. A. Sloane, Apr 06 2001

Keywords

• nonn
• tabf
• easy

Comments

(n,k)-graphs are simple graphs with n vertices and k edges.

Row indexed n has length 2n-3.

The diagonal counting the super edge-magic labelings of (n,n)-graphs appears to be A077613(n-1).

Examples

			1; 3,2,1; 6,6,6,4,2; 10,14,20,24,24,16,8; ...
		

Links

• Jason Kimberley, Rows n = 2..101 of triangle
• R. M. Figueroa-Centeno et al., The place of super edge-magic labelings among other classes of labelings, Discrete Math., 231 (2001), 153-168.

Programs

Magma

A060408 := func< n, k | &+[ Integers() | &*[ Integers() | a[j] : j in [i .. i+k-1] ] : i in [3 .. 2*n-k] ] where a is [ j lt 3 select 0 else j le n+1 select (j-1) div 2 else (2*n-j+1) div 2 : j in [1..2*n-1] ] >; [[ A060408(n,k): k in [1..2*n-3] ]: n in [1..10]];

Extensions

Entry T(3,3)=1 (that was erroneously missing from the table of Figueroa-Centeno et al. making the rows appear to be irregular) inserted by, DOI reference provided by, and empirical cross reference for the T(n,n) diagonal observed by Jason Kimberley, Apr 16 2010