Odd problem with sequence A108247

[Brendan McKay]

Ok, I think I figured it out.  There is a multi-step error.

(1) The values of A108247 should be 1, 2, 4720, 1256395, 699971370, ...
    as per the recurrence which appears there.

(2) The values  1, 1, 10, 760, 190050, 103050570, 102359800620, ...
    appearing incorrectly in A108247 are also listed for A108243.
    "a(n)= number of 3-Regular (trivalent) multi-graphs without loops
     on 2n vertices a(n)= number of symmetric 2nx2n matrices with
     {0,1,2}-entries with row sum equal to 3 for each row, and trace 0."
  --- However, the description has an error: {0,1,2} should be {0,1,2,3}.

(3) The description {0,1,2} that incorrectly appears on A108243, is
    the correct description of A109542.
    "a(n) = number of labeled 3-regular (trivalent) multi-graphs
    without self-loops on 2n vertices with a maximum of 2 edges
    between any pair of nodes. Also a(n) = number of labeled
    symmetric 2n X 2n matrices with {0,1,2}-entries with row sum
    equal to 3 for each row and trace 0."

Brendan.


* Brendan McKay <bdm at cs.anu.edu.au> [070401 23:28]:
> 
> Hello, there is a problem with sequence A108247.
> 
> A108247	  Number of 3-regular (trivalent) labeled graphs on 2n
> vertices with multiple edges and loops allowed.		
> 1, 1, 10, 760, 190050, 103050570, 102359800620, 168076482974400, ...
> Linear recurrence satisfied by a(n) {a(0) = 1, a(3) = 4720, a(4) =
> 1256395, a(5) = 699971370, a(1) = 2, a(2) = 47, and ...
> 
> See the problem?  The initial values in the Linear recurrence are
> 1, 2, 4720, 1256395, 699971370, ...
> which are not the same as listed for this sequence.
> 
> My computations suggest that 1, 2, 4720, 1256395, 699971370, ...
> matches the definition precisely. In fact it is A005814
> "Number of trivalent labeled graphs with 2n nodes."
> 
> So what does 1, 1, 10, 760, 190050, ... count?
> 
> Brendan.