[seqfan] Re: Mystery of A049476

[D. S. McNeil]

Okay, combining the quote that Neil posted with reading the paper and
comparing that with A049478 (the alleged size of the gap) made it clear
what's going on.  In retrospect the quote should have sufficed but I have
to admit it didn't until I read the relevant section of the paper. :-)

The size of a gap is the minimum number g such that the leftmost elements
of the row are the set {n,n-1...n-g} AND {n,n-1,...,n-g-1}, or
equivalently, the row starts with the set {n,n-1,...,n-g} and the next
element of the row is n-g-1.  If I understand the clear/break terminology
of the paper, this is the first break.  (It's been a surprisingly long day,
so I could have an offset wrong there in my description.)

Using this criterion and taking the record locations and values of g, I get:

(1, 0)
(2, 1)
(5, 4)
(13, 6)
(14, 12)
(26, 22)
(61, 27)
(63, 62)
(111, 64)
(131, 84)
(151, 104)
(153, 106)
(155, 108)
(161, 114)
(179, 132)
(295, 142)

where the first column is A049476 and the second is A049478.

I would have had zero chance of figuring out that this is what was meant by
"gap" without the additional information from Neil and the paper..


Doug