

A168238


Number of different 0moment rowing configurations for 4n rowers.


3



1, 4, 29, 263, 2724, 30554, 361677, 4454273, 56546511, 735298671, 9749613914, 131377492010, 1794546880363, 24798396567242, 346130144084641, 4873560434459530, 69149450121948083, 987844051312409668, 14198028410251734447, 205181815270346718199
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OFFSET

1,2


COMMENTS

Also the number of ways to assign 2n +1's and 2n 1's to the numbers 1,2,...,4n such that the sum is 0, assuming 1 gets the sign +1.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..50
John D. Barrow, Rowing and the SameSum Problem Have Their Moments, arXiv:0911.3551 [physics.popph], 20092010.


EXAMPLE

For n = 2 there are 4 solutions to the 8man rowing problem.
For n=1 the unique solution is 1+4 = 2+3. For n=2 there are 4 different solutions: 1+2+7+8 = 3+4+5+6, 1+3+6+8 = 2+4+5+7, 1+4+5+8 = 2+3+6+7, 1+4+6+7 = 2+3+5+8.  Michel Marcus, May 25 2013


MATHEMATICA

b[L_List] := b[L] = Module[{nL = Length[L], k = L[[1]], m = L[[2]]}, Which[L[[1]] == 0, If[nL == 3, 1, b[L[[2 ;; nL]]]], L[[1]] < 1, 0, True, Sum[If[L[[j]] < m, 0, b[Join[Sort[Table[L[[i]]  If[i == j, m + 1/97, 0], {i, 1, nL  2}]], {m  1, k}]]], {j, 1, nL  2}]]];
A[n_, k_] := If[n==0  k==0, 1, b[Join[Array[(k (n k + 1)/2 + k/97)&, n], {k n, k}]]/n!];
a[n_] := A[2, 2n];
Array[a, 20] (* JeanFrançois Alcover, Aug 19 2018, after Alois P. Heinz *)


CROSSREFS

Bisection of row n=2 of A203986.  Alois P. Heinz, Jan 09 2012
Cf. A227850.
Sequence in context: A203970 A250885 A244594 * A294160 A160885 A182356
Adjacent sequences: A168235 A168236 A168237 * A168239 A168240 A168241


KEYWORD

nonn


AUTHOR

Jeffrey Shallit, Nov 21 2009


EXTENSIONS

a(6)a(20) from Alois P. Heinz, Jan 09 2012


STATUS

approved



