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 A317445 Number of permutations of [n] whose lengths of increasing runs are distinct squares. 6
 1, 1, 0, 0, 1, 8, 0, 0, 0, 1, 18, 0, 0, 1428, 47998, 0, 1, 32, 0, 0, 9688, 505056, 0, 0, 0, 4085949, 284958912, 0, 0, 290824632172, 28643427712626, 0, 0, 0, 104902510, 9998016202, 1, 72, 23207824626842, 3008268832634364, 182778, 206173972520, 24290829974718, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA a(n) = 0 <=> n in { A001422 }. a(n) > 0 <=> n in { A003995 }. MAPLE g:= (n, s)-> `if`(n in s or not issqr(n), 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..50); CROSSREFS Cf. A000290, A001422, A003995, A317129, A317444, A317446, A317447, A317448. Sequence in context: A325737 A272625 A220667 * A199619 A036482 A273650 Adjacent sequences:  A317442 A317443 A317444 * A317446 A317447 A317448 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 28 2018 STATUS approved

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Last modified July 23 15:58 EDT 2019. Contains 325258 sequences. (Running on oeis4.)