A342307 - OEIS

A342307

Table read by ascending antidiagonals: T(n, k) is the maximum number of quasi k-gons that are not k-gons in a finite projective plane of order n, with k >= 3.

126, 936, 2520, 3780, 41184, 25200, 11160, 287280, 1029600, 151200, 27090, 1294560, 12927600, 18532800, 529200, 57456, 4442760, 90619200, 439538400, 259459200, 846720, 110376, 12640320, 444276000, 4893436800, 12307075200, 2905943040, 0, 196560, 31346784, 1706443200, 34653528000, 222651374400, 295369804800, 26153487360, 0

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OFFSET

2,1

LINKS

Table of n, a(n) for n=2..37.

Vladislav Taranchuk, On the number of k-gons in finite projective planes, (2020).

FORMULA

T(n, k) = k!*binomial(k - 1, 2)*binomial(n^2 + n + 1, k - 1)*(n - 1).

EXAMPLE

n\k | 3 4 5 6

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2 | 126 2520 25200 151200 ...