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A295946 Number of set partitions of [3n] into n subsets of size three such that all element sums are triangular numbers. 1
1, 1, 1, 2, 17, 149, 1439, 16993, 373393, 6899469, 214746442, 7287992421 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..11.

EXAMPLE

a(0) = 1: {}.

a(1) = 1: {{1,2,3}}.

a(2) = 1: {{1,2,3}, {4,5,6}}.

a(3) = 2: {{1,6,8}, {2,4,9}, {3,5,7}}, {{1,5,9}, {2,6,7}, {3,4,8}}.

a(4) = 17: {{1,2,12}, {3,8,10}, {4,6,11}, {5,7,9}}, {{1,2,12}, {3,7,11}, {4,8,9}, {5,6,10}}, {{1,3,11}, {2,9,10}, {4,5,12}, {6,7,8}}, {{1,6,8}, {2,9,10}, {3,7,11}, {4,5,12}}, {{1,9,11}, {2,3,10}, {4,5,12}, {6,7,8}}, {{1,9,11}, {2,6,7}, {3,8,10}, {4,5,12}}, {{1,4,10}, {2,8,11}, {3,6,12}, {5,7,9}}, {{1,5,9}, {2,8,11}, {3,6,12}, {4,7,10}}, {{1,9,11}, {2,5,8}, {3,6,12}, {4,7,10}}, {{1,3,11}, {2,7,12}, {4,8,9}, {5,6,10}}, {{1,5,9}, {2,7,12}, {3,8,10}, {4,6,11}}, {{1,9,11}, {2,7,12}, {3,4,8}, {5,6,10}}, {{1,9,11}, {2,7,12}, {3,8,10}, {4,5,6}}, {{1,8,12}, {2,3,10}, {4,6,11}, {5,7,9}}, {{1,8,12}, {2,9,10}, {3,5,7}, {4,6,11}}, {{1,8,12}, {2,4,9}, {3,7,11}, {5,6,10}}, {{1,8,12}, {2,9,10}, {3,7,11}, {4,5,6}}.

MAPLE

b:= proc(s) option remember; `if`(s={}, 1, (j->

      add(add(`if`(i<j and k<i and issqr((k+i+j)*8+1),

       b(s minus {k, i, j}), 0), k=s), i=s))(max(s)))

    end:

a:= n-> b({$1..3*n}):

seq(a(n), n=0..7);

CROSSREFS

Cf. A000217, A278329.

Sequence in context: A273340 A074624 A245807 * A176934 A126037 A241135

Adjacent sequences:  A295943 A295944 A295945 * A295947 A295948 A295949

KEYWORD

nonn,more

AUTHOR

Alois P. Heinz, Nov 30 2017

STATUS

approved

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Last modified May 25 22:17 EDT 2019. Contains 323576 sequences. (Running on oeis4.)