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 A317446 Number of permutations of [n] whose lengths of increasing runs are distinct triangular numbers. 6
 1, 1, 0, 1, 6, 0, 1, 12, 0, 166, 3687, 20, 0, 570, 18514, 1, 16044, 689458, 1630, 46150176, 2799527248, 108527, 6182180, 0, 653209572, 50529806020, 457774882, 592018, 64091958837, 5934158290988, 7151183666, 15132424235658, 1574449800015044, 0, 342747690810188908 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..160 FORMULA a(n) = 0 <=> n in { A053614 }. a(n) > 0 <=> n in { A061208 }. MAPLE g:= (n, s)-> `if`(n in s or not issqr(8*n+1), 0, 1): b:= proc(u, o, t, s) option remember; `if`(u+o=0, g(t, s),       `if`(g(t, s)=1, add(b(u-j, o+j-1, 1, s union {t})        , j=1..u), 0)+ add(b(u+j-1, o-j, t+1, s), j=1..o))     end: a:= n-> b(n, 0\$2, {}): seq(a(n), n=0..40); CROSSREFS Cf. A000217, A053614, A061208, A317130, A317444, A317445, A317447, A317448. Sequence in context: A320906 A195445 A215080 * A137943 A202189 A202183 Adjacent sequences:  A317443 A317444 A317445 * A317447 A317448 A317449 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 28 2018 STATUS approved

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Last modified September 18 09:22 EDT 2020. Contains 337166 sequences. (Running on oeis4.)