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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 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 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 January 21 16:47 EST 2020. Contains 331114 sequences. (Running on oeis4.)