cp's OEIS Frontend

A379686 a(n) = (a(n-1)+1)*(a(n-2)+1)*(a(n-3)+1)*(a(n-4)+1)/a(n-5), with a(1)=1, a(2)=2, a(3)=6, a(4)=42, a(5)=1806.

%I A379686 #29 Jan 12 2025 07:31:58
%S A379686 1,2,6,42,1806,1631721,443752508927,9376966151402427009536,
%T A379686 292117920945338351144537464770855449375232,
%U A379686 1098221126335915194898500730834145753769059346709551018699709189743396297017856
%N A379686 a(n) = (a(n-1)+1)*(a(n-2)+1)*(a(n-3)+1)*(a(n-4)+1)/a(n-5), with a(1)=1, a(2)=2, a(3)=6, a(4)=42, a(5)=1806.
%C A379686 Sequence consists of (positive) integers.
%C A379686 Values of a unitary Y-frieze pattern associated to the linearly oriented quiver K5 (i.e., the quiver whose underlying graph is the complete graph on the vertices {1,2,3,4,5}, oriented such that i -> j whenever i < j).
%H A379686 Seiichi Manyama, <a href="/A379686/b379686.txt">Table of n, a(n) for n = 1..14</a>
%H A379686 Antoine de Saint Germain, <a href="https://arxiv.org/abs/2311.03073">Y-frieze patterns</a>, arXiv:2311.03073 [math.CO], 2023.
%F A379686 a(n) = b(n+1) * b(n+2) * b(n+3) * b(n+4) where b is A072713. - _Andrey Zabolotskiy_, Jan 08 2025
%t A379686 a[1]=1;a[2]=2;a[3]=6;a[4]=42;a[5]=1806;a[n_]:=(a[n-1]+1)*(a[n-2]+1)*(a[n-3]+1)*(a[n-4]+1)/a[n-5];Table[a[n],{n,10}] (* _James C. McMahon_, Jan 08 2025 *)
%o A379686 (GAP) x := [1,2,6,42,1806]; for n in [1..15] do x[n+5] := (x[n+4]+1)*(x[n+3]+1)*(x[n+2]+1)*(x[n+1]+1)/x[n]; od;
%o A379686 (Magma) I:=[1, 2, 6, 42,1806]; [n le 5 select I[n] else (Self(n-1)+1)*(Self(n-2)+1)*(Self(n-3)+1)*(Self(n-4)+1)/Self(n-5): n in [1..15]]; // _Vincenzo Librandi_, Dec 31 2024
%Y A379686 Cf. A072713, A007018, A276453.
%K A379686 nonn
%O A379686 1,2
%A A379686 _Antoine de Saint Germain_, Dec 29 2024