A276453 - OEIS

%I #28 Dec 31 2024 11:14:44

%S 1,1,2,6,42,903,136052,881442036,2581196224947732,

%T 342795531574625708871288171,

%U 5732512385084161208637718426682572229606557631,5754497648510061274107897581706624823818534711463525598519384262130236399970112

%N a(n) = (a(n-1)+1)*(a(n-2)+1)*(a(n-3)+1)/a(n-4) with a(0) = a(1) = 1, a(2) = 2, a(3) = 6.

%C From _Antoine de Saint Germain_, Dec 30 2024: (Start)

%C Sequence consists of integers, see Math StackExchange link.

%C Values of a unitary Y-frieze pattern associated to the linearly oriented quiver K4 (i.e., the quiver whose underlying graph is the complete graph on the vertices {1,2,3,4}, oriented such that i -> j whenever i < j). (End)

%H Seiichi Manyama, <a href="/A276453/b276453.txt">Table of n, a(n) for n = 0..15</a>

%H Math StackExchange, <a href="https://math.stackexchange.com/questions/1905063/is-a276175-integer-only/4941736#4941736">Is A276175 integer-only?</a>

%F a(n) = A051786(n)*A051786(n+1)*A051786(n+2).

%t RecurrenceTable[{a[n] == (a[n - 1] + 1) (a[n - 2] + 1) (a[n - 3] + 1)/a[n - 4], a[0] == 1, a[1] == 1, a[2] == 2, a[3] == 6}, a, {n, 0, 11}] (* _Michael De Vlieger_, Sep 03 2016 *)

%o (Ruby)

%o def A276453(n)

%o   a = [1, 1, 2, 6]

%o   ary = [1]

%o   while ary.size < n + 1

%o     i = a[1..-1].inject(1){|s, i| s * (i + 1)}

%o     break if i % a[0] > 0

%o     a = *a[1..-1], i / a[0]

%o     ary << a[0]

%o   end

%o   ary

%o end

%o (Magma) I:=[1, 1, 2, 6]; [n le 4 select I[n] else (Self(n-1)+1)*(Self(n-2)+1)*(Self(n-3)+1)/Self(n-4): n in [1..13]]; // _Vincenzo Librandi_, Dec 30 2024

%Y Cf. A051786, A101879, A276175.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 03 2016