cp's OEIS Frontend

A247550 Number of 1 up, 1 down, 2 up, 1 down, 3 up, 1 down, ... permutations of [n].

%I A247550 #13 Mar 26 2021 12:36:35
%S A247550 1,1,1,2,5,9,40,169,477,1099,8766,56341,234717,774279,2182270,
%T A247550 27260478,249339033,1457282467,6624389780,25274016620,84400336507,
%U A247550 1518975557185,18799199683021,147690564521818,892559422156897,4474464873070564,19410417198316364
%N A247550 Number of 1 up, 1 down, 2 up, 1 down, 3 up, 1 down, ... permutations of [n].
%H A247550 Alois P. Heinz, <a href="/A247550/b247550.txt">Table of n, a(n) for n = 0..275</a>
%e A247550 a(5) = 9: 13245, 14235, 15234, 23145, 24135, 25134, 34125, 35124, 45123.
%e A247550 a(6) = 40: 132465, 132564, 142365, 142563, 143562, 152364, 152463, 153462, 162354, 162453, 163452, 231465, 231564, 241365, 241563, 243561, 251364, 251463, 253461, 261354, 261453, 263451, 341265, 341562, 342561, 351264, 351462, 352461, 361254, 361452, 362451, 451263, 451362, 452361, 461253, 461352, 462351, 561243, 561342, 562341.
%p A247550 b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1, `if`(t>0,
%p A247550        add(b(u+j-1, o-j, `if`(t=k, 0, t+1), k), j=1..o),
%p A247550        add(b(u-j, o+j-1, 1, k+1), j=1..u)))
%p A247550     end:
%p A247550 a:= n-> b(n, 0$3):
%p A247550 seq(a(n), n=0..35);
%t A247550 b[u_, o_, t_, k_] := b[u, o, t, k] = If[u + o == 0, 1, If[t > 0,
%t A247550      Sum[b[u + j - 1, o - j, If[t == k, 0, t + 1], k], {j, 1, o}],
%t A247550      Sum[b[u - j, o + j - 1, 1, k + 1], {j, 1, u}]]];
%t A247550 a[n_] := b[n, 0, 0, 0];
%t A247550 a /@ Range[0, 35] (* _Jean-François Alcover_, Mar 26 2021, after _Alois P. Heinz_ *)
%Y A247550 Cf. A229551.
%K A247550 nonn
%O A247550 0,4
%A A247550 _Alois P. Heinz_, Sep 19 2014