Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 May 05 2020 19:25:45
%S 0,5,156,2114,19328,140571,882340,5007112,26441856,132439905,
%T 637468300,2976161790,13569454592,60725449335,267757190100,
%U 1166662948900,5034645823680,21556696454685,91704869986620,388044105102650,1634678955350400,6860481786528275,28700914012807556
%N Number of permutations of 1..n arranged in a circle with exactly 4 adjacent element pairs in decreasing order.
%H Andrew Howroyd, <a href="/A151577/b151577.txt">Table of n, a(n) for n = 4..500</a>
%F From _Andrew Howroyd_, May 05 2020: (Start)
%F a(n) = n*A000498(n-1).
%F a(n) = n*(4^(n-1) - n*3^(n-1) + binomial(n,2)*2^(n-1) - binomial(n,3)). (End)
%o (PARI) a(n) = {n*(4^(n-1) - n*3^(n-1) + binomial(n,2)*2^(n-1) - binomial(n,3))} \\ _Andrew Howroyd_, May 05 2020
%Y Column k=4 of A334218.
%Y Cf. A000498.
%K nonn
%O 4,2
%A _R. H. Hardin_, May 21 2009
%E Terms a(17) and beyond from _Andrew Howroyd_, May 05 2020