A172572 Number of 3*n X 6 0..1 arrays with row sums 2 and column sums n.

90, 67950, 90291600, 154700988750, 306407299538340, 666569141498660400, 1548539246648239560000, 3776577900841430197548750, 9561215418596022668009737500, 24935177268489106332174087326700

Offset

1,1

Links

Christoph Koutschan, Table of n, a(n) for n = 1..75 (first 33 terms from R. H. Hardin)

Manuel Kauers and Christoph Koutschan, Some D-finite and some possibly D-finite sequences in the OEIS, arXiv:2303.02793 [cs.SC], 2023, pp. 19-23.

Formula

Conjectured recurrence of order 3 and degree 9: (n + 2)*(n + 3)^5*(2*n + 5)*(62*n^2 + 217*n + 191)*a(n + 3) - 9*(n + 2)*(3*n + 7)*(3*n + 8)*(5084*n^6 + 68634*n^5 + 383756*n^4 + 1137319*n^3 + 1884032*n^2 + 1653960*n + 601185)*a(n + 2) - 9*(3*n + 4)*(3*n + 5)*(3*n + 7)*(3*n + 8)*(31372*n^5 + 313720*n^4 + 1227805*n^3 + 2354425*n^2 + 2220988*n + 827860)*a(n + 1) + 20250*(n + 1)*(3*n + 1)*(3*n + 2)*(3*n + 4)*(3*n + 5)*(3*n + 7)*(3*n + 8)*(62*n^2 + 341*n + 470)*a(n) = 0. - Christoph Koutschan, Feb 26 2023

Conjecture: a(n) ~ 3^(3*n + 1/2) * 5^(3*n + 5/2) / (128 * Pi^(5/2) * n^(5/2)), based on the recurrence by Christoph Koutschan. - Vaclav Kotesovec, Feb 26 2023

Mathematica

Walks6D[n_Integer, steps_List] := Walks6D[n, steps] =
Module[{vals = {{{{{1}}}}}, seq = {}, n0, n1},
  Do[
    vals = Table[
      n0 = Ceiling[(nsum - n1 - n2 - n3 - n4)/2];
      Join[
        Table[0, {n0}],
        Table[Total[Function[s,
            pos = Reverse[Sort[{n1, n2, n3, n4, n5, nsum - n1 - n2 - n3 - n4 - n5} - s]];
            If[Min[pos] < 0, 0, vals[[##]]& @@ Most[pos + 1]]] /@ steps],
          {n5, n0, Min[n4, nsum - n1 - n2 - n3 - n4]}]
      ],
      {n1, 0, Min[n, nsum]},
      {n2, 0, Min[n1, nsum - n1]},
      {n3, 0, Min[n2, nsum - n1 - n2]},
      {n4, 0, Min[n3, nsum - n1 - n2 - n3]}];
    If[IntegerQ[n1 = nsum/6 + 1], AppendTo[seq, vals[[n1, n1, n1, n1, n1]]]],
  {nsum, 2, 6 n, 2}];
  Return[seq];
];
Walks6D[20, Permutations[{1, 1, 0, 0, 0, 0}]] (* Christoph Koutschan, Feb 26 2023 *)

Crossrefs

Sequence in context: A145413 A367459 A279442 * A052277 A172671 A066784

Adjacent sequences: A172569 A172570 A172571 * A172573 A172574 A172575

Keyword

nonn

Author

R. H. Hardin, Feb 06 2010

Status

approved