A005983 -id:A005983 - cp's OEIS frontend

A229885 Number of 4 up, 4 down permutations of [n].

1, 1, 1, 1, 1, 1, 5, 15, 35, 70, 574, 2674, 9274, 26599, 305747, 1944033, 8995805, 33757360, 498851248, 4017418768, 23236611280, 107709888805, 1945409895065, 18965460022971, 131635127294783, 726401013530416, 15505381392117616, 177447751441161616

Offset: 0

Alois P. Heinz, Oct 02 2013

Limit n->infinity (a(n)/n!)^(1/n) = 0.38605986196... . - Vaclav Kotesovec, Sep 06 2014

			a(5) = 1: 12345.
a(6) = 5: 123465, 123564, 124563, 134562, 234561.
a(7) = 15: 1234765, 1235764, 1236754, 1245763, 1246753, 1256743, 1345762, 1346752, 1356742, 1456732, 2345761, 2346751, 2356741, 2456731, 3456721.

Alois P. Heinz, Table of n, a(n) for n = 0..200

Column k=4 of A229892.

Cf. A005983.

b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(`if`(t=4,
       b(o-j, u+j-1, 1), b(u+j-1, o-j, t+1)), j=1..o))
    end:
a:= n-> b(0, n, 0):
seq(a(n), n=0..30);

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Sum[If[t == 4, b[o - j, u + j - 1, 1], b[u + j - 1, o - j, t + 1]], {j, 1, o}]];
a[n_] := b[0, n, 0];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 21 2020, after Alois P. Heinz *)

A259452 Number of 5 up, 5 down, 5 up, ... permutations of length 5n+1.

Original entry on oeis.org

1, 1, 252, 578005, 6190034016, 214265281290061, 19157603395806362772, 3800502511986185228829385, 1498722661993096106927612109936, 1081056808393919319749313795137642521, 1336319624105519211256870506149168604698792

Offset: 0

N. J. A. Sloane, Jun 28 2015

nonn

P. R. Stein, personal communication.

Alois P. Heinz, Table of n, a(n) for n = 0..100
P. R. Stein & N. J. A. Sloane, Correspondence, 1975

Cf. A005981-A005983.

b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(`if`(
       t=5, b(o-j, u+j-1, 1), b(u+j-1, o-j, t+1)), j=1..o))
    end:
a:= n-> b(0, 5*n+1, 0):
seq(a(n), n=0..10);  # Alois P. Heinz, Jul 02 2015

k = 5; b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Sum[If[t == k, b[o - j, u + j - 1, 1], b[u + j - 1, o - j, t + 1]], {j, 1, o}]]; Array[b[0, k # + 1, 0] &, 10] (* Michael De Vlieger, Oct 15 2017, after Jean-François Alcover at A005983 *)

More terms from Alois P. Heinz, Jul 02 2015

cp's OEIS Frontend

A229885 Number of 4 up, 4 down permutations of [n].

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