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A230132 Number of permutations of order n with the length of longest run equal 9. 3
2, 36, 574, 9024, 145080, 2419872, 42129360, 767370240, 14631376500, 291914163322, 6088804487138, 132624737931726, 3012939864521998, 71296697740927172, 1755099895042102380, 44889002698811118240, 1191389820174200208622, 32774409073391657243622 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 9..450

MAPLE

g:= proc(u, o, t) option remember; `if`(u+o=0, 1,

       add(g(o+j-1, u-j, 2), j=1..u) +`if`(t<9,

       add(g(u+j-1, o-j, t+1), j=1..o), 0))

    end:

b:= proc(u, o, t) option remember; `if`(t=9, g(u, o, t),

       add(b(o+j-1, u-j, 2), j=1..u)+

       add(b(u+j-1, o-j, t+1), j=1..o))

    end:

a:= n-> add(b(j-1, n-j, 1), j=1..n):

seq(a(n), n=9..30);

MATHEMATICA

length = 9;

g[u_, o_, t_] := g[u, o, t] = If[u+o == 0, 1, Sum[g[o + j - 1, u - j, 2], {j, 1, u}] + If[t<length, Sum[g[u + j - 1, o - j, t+1], {j, 1, o}], 0]];

b[u_, o_, t_] := b[u, o, t] = If[t == length, g[u, o, t], Sum[b[o + j - 1, u - j, 2], {j, 1, u}] + Sum[b[u + j - 1, o - j, t + 1], {j, 1, o}]];

a[n_] := Sum[b[j - 1, n - j, 1], {j, 1, n}];

Table[a[n], {n, length, 30}] (* Jean-Fran├žois Alcover, Aug 18 2018, after Alois P. Heinz *)

CROSSREFS

Column l=9 of A211318.

A diagonal of A010026.

Sequence in context: A139738 A248343 A025608 * A141132 A064030 A228790

Adjacent sequences:  A230129 A230130 A230131 * A230133 A230134 A230135

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 10 2013

STATUS

approved

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Last modified April 16 23:40 EDT 2021. Contains 343051 sequences. (Running on oeis4.)