[seqfan] Independent confirmation of floretion iteration for A113249, and (almost) A090390
Robert Munafo
mrob27 at gmail.com
Fri Nov 20 22:19:27 CET 2009
Thanks to Creighton's latest message to me, I have enough to actually
write my own code and test things.
I have added his basic definitions to my web page:
mrob.com/pub/math/seq-floretion.html Once again I reordered things to
make it easier for my readers.
I have also been able to calculate A113249, and I almost have A090390.
There is C source code on the same web page. Here is the output:
Calculating A113249 :
A = 1 'i -1 'k +1 i' -1 k' -3 'jj' -1 'ij' -1 'ji' -1 'jk' -1 'kj'
B = +0.5 'kk' +0.5 'ij' +0.5 'ji' +0.5
X = 1 'i -1.5 'k +1 i' -1.5 k' -0.5 'ii' -2.5 'jj' +1 'kk' -1 'jk' -1 'kj' -1
tesseq(X) == 1, -1, 4, 11, 1, 59, 484, -1009, 6241, -2761, 13924,
87251, 57121, 49139, 4072324, -7165609, 35058241, 10350959, 30492484,
559712411, 973502401, -1957852501, 30450948004, -41421000289,
174055005601, 241428053159, 9658565284, 2872244917091, 11300885699041,
-25300162140061, 205383809363524, ...
Calculating A090390 :
X = -0.5 'j +0.5 'k -0.5 j' +0.5 k' -2 'ii' +1 'jj' -1 'kk' +0.5 'ij'
+0.5 'ik' +0.5 'ji' +1 'jk' +0.5 'ki' +1 'kj' +1
tesseq(X) == 1, 1, 9, 49.5, 293, 1711.75, 10022.5, 58657.375,
343304.5, 2009151.4375, 11757860.625, 68805896.34375, 402629090.75,
2355955113.10938, 13785149942.5938, 80656401186.8359,
471899251236.906, 2760851655596.09, 16151781130740.4,
94489066839998.6, 552747401757504, ...
Notice that the output for A090390 is wrong from the "49" term onward.
It appears to be a truncation or roundoff issue. A113249 does not
encounter this issue even as the terms get fairly large. I suspect
A090390 is not actually tesseq() of the vector specified in the OEIS
entry, and that some type of integer rounding operation was being
used. I haven't found any references to truncation, rounding, "floor"
or "ceil" in Creighton's writing so far, except his 2009 paper, page
29, which is clearly unrelated.
More to come...
I'd eventually like to link some of the sequences to my page. I think
it makes sense to link to different places on my page according to the
iterative function being used, for example all the tesseq()
definitions can link to what I have written so far. Let me know what
makes sense -- I can easily create lists of A-numbers to give to Neil.
As I mentioned before, I can also provide a complete list of
"crowdog(dot)de" links from December 2005.
--
Robert Munafo -- mrob.com
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