[seqfan] Confused about A144204
Alonso Del Arte
alonso.delarte at gmail.com
Thu Jul 9 23:12:05 CEST 2009
I was thinking about the triangle determined by a(n, k) = nk - (n +
k), so I had Mathematica calculate it to ten rows with this code:
a[n_, k_] := a[n, k] = n*k - (n + k); ColumnForm[Table[a[n, k], {n,
10}, {k, n}], Center]
-1
-1, 0
-1, 1, 3
-1, 2, 5, 8
-1, 3, 7, 11, 15
-1, 4, 9, 14, 19, 24
-1, 5, 11, 17, 23, 29, 35
-1, 6, 13, 20, 27, 34, 41, 48
-1, 7, 15, 23, 31, 39, 47, 55, 63
-1, 8, 17, 26, 35, 44, 53, 62, 71, 80
I looked up the fifth row and A144204 came up as a result. But the
definition for that sequence is "Arises in complete intersection
threefolds, Array A[k,n] = (n+k-2)*(n-1) - 1 by antidiagonals." I'm
not exactly sure how the formula (n + k - 2)(n - 1) - 1 gives the
triangle quoted above. Just plugging it into the code above gives a
somewhat different triangle. I do admit that I'm confused by
"antidiagonal," which should be a fairly basic term.
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