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

Author

Antal Pinter, Dec 31 2015

Keywords

• nonn
• easy

Comments

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.

Links

• 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.

Crossrefs

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

Programs

Magma

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

Mathematica

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

Formula

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