User:Jason Kimberley/A060408

A060408

%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

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

%C A060408 Row n has length 2n-3.

%C A060408 The diagonal counting the number of super edge-magic labellings of (n,n)-graphs appears to be A077613.

%D A060408 R. M. Figueroa-Centeno et al., The place of super edge-magic labelings among other classes of labelings, Discrete Math., 231 (2001), 153-168.

%e A060408 1; 3,2,1; 6,6,6,4,2; 10,14,20,24,24,16,8; ...

%K A060408 nonn,tabf

%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]
   ]
 >
;

%O A060408 2,2

%A A060408 N. J. A. Sloane (njas(AT)research.att.com), Apr 06 2001

---

Entering the Magma code above and

[[A060408(n,k): k in [1..2*n-3] ]: n in [1..10]];

into the Magma Calculator produced the following output:

Magma V2.16-1     Sun Jan  3 2010 19:40:00    [Seed = 706819820]
   -------------------------------------

[
    [],
    [ 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 ],
    [ 36, 100, 304, 920, 2688, 7272, 18144, 40320, 80640, 138240, 207360, 248832, 248832, 165888, 82944 ],
    [ 45, 140, 480, 1656, 5600, 17832, 53280, 145152, 362880, 806400, 1612800, 2764800, 4147200, 4976640, 4976640, 3317760, 1658880 ]
]

Total time: 0.270 seconds, Total memory usage: 8.00MB