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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.)