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

0,2

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

Table of n, a(n) for n=0..27.

OEIS Wiki, Square hyperpyramidal numbers, line d=12 of first table.

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A161475 A162301 A161862 * A370962 A222369 A131709

Adjacent sequences: A266558 A266559 A266560 * A266562 A266563 A266564

Keyword

nonn,easy

Author

Antal Pinter, Dec 31 2015

Status

approved