I am trying to do some research on alcuin's sequence, but all the
references that I can find quote the terms of the sequence as the
coefficients in the Maclaurin expansion of [(1-x^2)(1-x^3)(1-x^4)]^-
1. I find this surprising, as I believe the sequence to have been
named after Alcuin of York (735-804) who lived many years before
Maclaurin expansions were discovered.
This sequence also gives the number of different triangles that have
integral sides and perimeter n. I would think that it is much more
likely that this is what Alcuin discovered, and years later someone
found that the above expansion acted as a generating function.
That is, of course, if the Alcuin who the sequence is named after is
Alcuin of York and not someone else with the same name.
I would be most grateful if you could either confirm or refute this,
or point me in the direction of any references.
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