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.

1, 2, 6, 42, 1806, 1631721, 443752508927, 9376966151402427009536, 292117920945338351144537464770855449375232, 1098221126335915194898500730834145753769059346709551018699709189743396297017856

Offset

1,2

Comments

Sequence consists of (positive) integers.

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).

Links

Seiichi Manyama, Table of n, a(n) for n = 1..14

Antoine de Saint Germain, Y-frieze patterns, arXiv:2311.03073 [math.CO], 2023.

Formula

a(n) = b(n+1) * b(n+2) * b(n+3) * b(n+4) where b is A072713. - Andrey Zabolotskiy, Jan 08 2025

Mathematica

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 *)

Prog

(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;
(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

Crossrefs

Cf. A072713, A007018, A276453.

Sequence in context: A054377 A349193 A230311 * A276416 A007018 A100016

Adjacent sequences: A379683 A379684 A379685 * A379687 A379688 A379689

Keyword

nonn

Author

Antoine de Saint Germain, Dec 29 2024

Status

approved