A094943 / A sequence generated from a semi-magic square

[Gottfried Helms]

Seqfans -

Am 25.08.05 19:49 schrieb Gottfried Helms:
>
> If the matrix-method given in the example below can be extended to higher
> order, then this would be a much more handy rule to compute the coefficients
> than to employ a symbolic algebra program and evaluate the nominator for
> higher orders ...
>
>
That seems to be possible. With order 4 and the "magic square"
      a :
     	|        1         4         3         2 |
     	|        2         1         4         3 |
     	|        3         2         1         4 |
     	|        4         3         2         1 |

I reproduce the values for the order-4-sequence with parameters
(a,b,c,d)=(1,2,3,4) and w = i (w0 = 1,w1 = i, w2 = -1, w3 = -i):


 1 ,
 26 ,
 256 ,
 2472 ,
 25056 ,

 250016 ,
 2499456 ,
 25002112 ,
 249995776 ,
 2500000256 ,

 25000032256 ,
 249999869952 ,
 2500000260096 ,
 25000000004096 ,
 249999997894656 ,

 2500000008404992 ,
 24999999983190016 ,
 250000000000065536 ,
 2500000000134086656 ,
 24999999999463391232 ,

 250000000001073217536 ,
 2500000000000001048576 ,
 24999999999991407968256

which approximates the ratio 10/1 between subsequent elements.
Nice... ;-)

Gottfried Helms