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A250263 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 7).

%I A250263 #12 Sep 03 2021 01:51:30
%S A250263 1,1,1,2,3,4,5,6,7,55,306,1145,3454,8997,21008,45031,630421,5954062,
%T A250263 36439007,174011100,697278853,2442137774,7677528495,154507257827,
%U A250263 2060124800270,17511127577941,114431145225190,619024078342189,2890746049056048,11979440405949527
%N A250263 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 7).
%H A250263 Alois P. Heinz, <a href="/A250263/b250263.txt">Table of n, a(n) for n = 0..500</a>
%p A250263 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A250263      `if`(t=1, add(b(u-j, o+j-1, irem(t+1, 7)), j=1..u),
%p A250263                add(b(u+j-1, o-j, irem(t+1, 7)), j=1..o)))
%p A250263     end:
%p A250263 a:= n-> b(0, n, 0):
%p A250263 seq(a(n), n=0..35);
%t A250263 b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, If[t == 1, Sum[b[u - j, o + j - 1, Mod[t + 1, 7]], {j, 1, u}], Sum[b[u + j - 1, o - j, Mod[t + 1, 7]], {j, 1, o}]]];
%t A250263 a[n_] := b[0, n, 0];
%t A250263 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Jul 22 2019, after _Alois P. Heinz_ *)
%Y A250263 Column k=7 of A250261.
%K A250263 nonn
%O A250263 0,4
%A A250263 _Alois P. Heinz_, Nov 15 2014