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

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
----+-------------------------------------
  2 |   126     2520     25200      151200 ...
  3 |   936    41184   1029600    18532800 ...
  4 |  3780   287280  12927600   439538400 ...
  5 | 11160  1294560  90619200  4893436800 ...
...

Mathematica

T[n_, k_]:=k!Binomial[k-1, 2]Binomial[n^2+n+1, k-1](n-1); Table[T[n-k+3, k], {n, 2, 9}, {k, 3, n+1}]//Flatten

Crossrefs

Cf. A000142, A000217, A000794, A001231, A124278, A124287, A293819.

Sequence in context: A292981 A126170 A324709 * A151989 A318626 A104678

Adjacent sequences: A342304 A342305 A342306 * A342308 A342309 A342310

Keyword

nonn,tabl

Author

Stefano Spezia, Mar 08 2021

Status

approved