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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.)