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
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
KEYWORD
nonn,easy
AUTHOR
Antal Pinter, Dec 31 2015
STATUS
approved