A168238 Number of different 0-moment rowing configurations for 4n rowers.

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

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 Same-Sum Problem Have Their Moments, arXiv:0911.3551 [physics.pop-ph], 2009-2010.

Example

For n = 2 there are 4 solutions to the 8-man 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] (* Jean-François 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: A250885 A369215 A244594 * A370955 A294160 A160885

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