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