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 A317130 Number of permutations of [n] whose lengths of increasing runs are triangular numbers. 8
 1, 1, 1, 2, 7, 24, 93, 483, 2832, 17515, 123226, 978405, 8312802, 75966887, 756376739, 8070649675, 91320842018, 1099612368110, 14054043139523, 189320856378432, 2682416347625463, 39945105092501742, 623240458310527252, 10160826473676346731, 172871969109661492526 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..400 EXAMPLE a(2) = 1: 21. a(3) = 2: 123, 321. a(4) = 7: 1243, 1342, 2134, 2341, 3124, 4123, 4321. a(5) = 24: 12543, 13542, 14532, 21354, 21453, 23541, 24531, 31254, 31452, 32145, 32451, 34521, 41253, 41352, 42135, 42351, 43125, 51243, 51342, 52134, 52341, 53124, 54123, 54321. MAPLE g:= n-> `if`(issqr(8*n+1), 1, 0): b:= proc(u, o, t) option remember; `if`(u+o=0, g(t),       `if`(g(t)=1, add(b(u-j, o+j-1, 1), j=1..u), 0)+        add(b(u+j-1, o-j, t+1), j=1..o))     end: a:= n-> b(n, 0\$2): seq(a(n), n=0..27); CROSSREFS Cf. A000217, A097597, A193374, A317111, A317128, A317129, A317131, A317132, A317446. Sequence in context: A150405 A150406 A150407 * A150408 A150409 A150410 Adjacent sequences:  A317127 A317128 A317129 * A317131 A317132 A317133 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 21 2018 STATUS approved

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Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)