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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.

%I A060408 #23 Sep 08 2022 08:45:03
%S A060408 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,
%T A060408 21,44,99,212,420,720,1080,1296,1296,864,432,28,68,180,464,1140,2520,
%U A060408 5040,8640,12960,15552,15552,10368,5184
%N 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.
%C A060408 (n,k)-graphs are simple graphs with n vertices and k edges.
%C A060408 Row indexed n has length 2n-3.
%C A060408 The diagonal counting the super edge-magic labelings of (n,n)-graphs appears to be A077613(n-1).
%H A060408 Jason Kimberley, <a href="/A060408/b060408.txt">Rows n = 2..101 of triangle</a>
%H A060408 R. M. Figueroa-Centeno et al., <a href="http://dx.doi.org/10.1016/S0012-365X(00)00314-9">The place of super edge-magic labelings among other classes of labelings</a>, Discrete Math., 231 (2001), 153-168.
%e A060408 1; 3,2,1; 6,6,6,4,2; 10,14,20,24,24,16,8; ...
%o A060408 (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]];
%K A060408 nonn,tabf,easy
%O A060408 2,2
%A A060408 _N. J. A. Sloane_, Apr 06 2001
%E A060408 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