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User: Antal Pinter

Antal Pinter has authored 2 sequences.

A266561 12-dimensional square numbers.

1, 14, 104, 546, 2275, 8008, 24752, 68952, 176358, 419900, 940576, 1998724, 4056234, 7904456, 14858000, 27041560, 47805615, 82317690, 138389160, 227613750, 366913365, 580610160, 903171360, 1382805840, 2086129500, 3104160696, 4559958144, 6618272584

Offset: 0

Antal Pinter, Dec 31 2015

2*a(n) is number of ways to place 11 queens on an (n+11) X (n+11) chessboard so that they diagonally attack each other exactly 55 times. The maximal possible attack number, p=binomial(k,2)=55 for k=11 queens, is achievable only when all queens are on the same diagonal. In graph-theory representation they thus form the corresponding complete graph.

Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 15.
OEIS Wiki, Square hyperpyramidal numbers, line d=12 of first table.

Cf. A000330, A002415, A005585, A040977, A050486, A053347, A054333, A054334, A057788.

[Binomial(n+11,11)*(n+6)/6: n in [0..40]]; // Vincenzo Librandi, Jan 01 2016

CoefficientList[Series[(1 + x)/(1 - x)^13, {x, 0, 33}], x] (* Vincenzo Librandi, Jan 01 2016 *)

a(n) = binomial(n+11,11)*(n+6)/6.
a(n) = 2*binomial(n+12,12) - binomial(n+11,11).
a(n) = binomial(n+11,11) + 2*binomial(n+11,12) for n>0.
G.f.: (1+x)/(1-x)^13. - Vincenzo Librandi, Jan 01 2016

A252593 Number of ways to place 8 nonattacking queens on an n X n board.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 92, 13848, 636524, 14803480, 207667564, 2008758532, 14752426528, 87154016752, 432539436508, 1858901487620

Offset: 1

Antal Pinter, Dec 18 2014

Conjectured recurrence order is 477 (see "Non-attacking chess pieces", p. 19). - Vaclav Kotesovec, Dec 19 2014

S. Chaiken, C. R. H. Hanusa and T. Zaslavsky, A q-Queens Problem, I. General theory, arXiv:1303.1879 [math.CO], 2013-2014.
V. Kotesovec, Non-attacking chess pieces, 6ed, 2013
Antal Pinter, Combinatorics, software for enumerating positions of non-attacking chess pieces.
I. Rivin, I. Vardi and P. Zimmermann, The n-queens problem, Amer. Math. Monthly, 101 (1994), 629-639.

Cf. A000170, A036464, A047659, A061994, A108792, A176186, A178721.

Column k=8 of A348129.

a(n) = n^16/40320 - n^15/432 + 221*n^14/2160 + O(n^13). - Vaclav Kotesovec, Dec 19 2014

a(16) from Vaclav Kotesovec, Dec 19 2014

a(17) from Vaclav Kotesovec, Dec 20 2014

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User: Antal Pinter

A266561 12-dimensional square numbers.

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