A278329 Number of set partitions of [3n] into n subsets of size three such that all element sums are squares.

1, 0, 0, 0, 0, 29, 35, 340, 26579, 390480, 9514434, 145963193, 5474045270, 87251356528

Offset

0,6

Links

Table of n, a(n) for n=0..13.

Example

a(5) = 29: {{1,3,5}, {2,9,14}, {4,6,15}, {7,8,10}, {11,12,13}},
  {{1,3,5}, {2,11,12}, {4,6,15}, {7,8,10}, {9,13,14}},
  {{1,2,6}, {3,7,15}, {4,8,13}, {5,9,11}, {10,12,14}},
  {{1,2,6}, {3,7,15}, {4,10,11}, {5,8,12}, {9,13,14}},
  {{1,3,5}, {2,8,15}, {4,7,14}, {6,9,10}, {11,12,13}},
  {{1,3,5}, {2,8,15}, {4,10,11}, {6,7,12}, {9,13,14}},
  {{1,9,15}, {2,3,4}, {5,6,14}, {7,8,10}, {11,12,13}},
  {{1,9,15}, {2,3,4}, {5,7,13}, {6,8,11}, {10,12,14}},
  {{1,2,6}, {3,9,13}, {4,7,14}, {5,8,12}, {10,11,15}},
  {{1,2,6}, {3,8,14}, {4,9,12}, {5,7,13}, {10,11,15}},
  {{1,3,5}, {2,9,14}, {4,8,13}, {6,7,12}, {10,11,15}},
  {{1,3,12}, {2,6,8}, {4,5,7}, {9,13,14}, {10,11,15}},
  {{1,11,13}, {2,3,4}, {5,6,14}, {7,8,10}, {9,12,15}},
  {{1,3,5}, {2,10,13}, {4,7,14}, {6,8,11}, {9,12,15}},
  {{1,2,6}, {3,8,14}, {4,10,11}, {5,7,13}, {9,12,15}},
  {{1,10,14}, {2,3,4}, {5,7,13}, {6,8,11}, {9,12,15}},
  {{1,2,6}, {3,10,12}, {4,7,14}, {5,9,11}, {8,13,15}},
  {{1,3,5}, {2,11,12}, {4,7,14}, {6,9,10}, {8,13,15}},
  {{1,3,5}, {2,9,14}, {4,10,11}, {6,7,12}, {8,13,15}},
  {{1,10,14}, {2,3,4}, {5,9,11}, {6,7,12}, {8,13,15}},
  {{1,6,9}, {2,3,11}, {4,5,7}, {8,13,15}, {10,12,14}},
  {{1,4,11}, {2,5,9}, {3,6,7}, {8,13,15}, {10,12,14}},
  {{1,2,6}, {3,10,12}, {4,8,13}, {5,9,11}, {7,14,15}},
  {{1,3,5}, {2,11,12}, {4,8,13}, {6,9,10}, {7,14,15}},
  {{1,2,6}, {3,9,13}, {4,10,11}, {5,8,12}, {7,14,15}},
  {{1,3,5}, {2,10,13}, {4,9,12}, {6,8,11}, {7,14,15}},
  {{1,11,13}, {2,3,4}, {5,8,12}, {6,9,10}, {7,14,15}},
  {{1,6,9}, {2,4,10}, {3,5,8}, {7,14,15}, {11,12,13}},
  {{1,5,10}, {2,6,8}, {3,4,9}, {7,14,15}, {11,12,13}}.

Mathematica

A278329[0] = 1;
A278329[n_] := Length@FindClique[Graph[First@# <-> Last@# & /@ Select[Subsets[Select[Flatten[IntegerPartitions[#^2, {3}, Range[3 n]] & /@ Range[Sqrt[9 n - 3]], 1], DuplicateFreeQ], {2}], DuplicateFreeQ@Flatten@# &]], {n}, All] (* Davin Park, Jan 26 2017 *)

Crossrefs

Cf. A000290, A252897, A278339, A281706, A295946.

Sequence in context: A039307 A043130 A043910 * A172413 A134254 A089296

Adjacent sequences: A278326 A278327 A278328 * A278330 A278331 A278332

Keyword

nonn,more

Author

Alois P. Heinz, Nov 18 2016

Extensions

a(12)-a(13) from Bert Dobbelaere, Apr 12 2019

Status

approved