A276453 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.

1, 1, 2, 6, 42, 903, 136052, 881442036, 2581196224947732, 342795531574625708871288171, 5732512385084161208637718426682572229606557631, 5754497648510061274107897581706624823818534711463525598519384262130236399970112

Offset: 0

Author

Seiichi Manyama, Sep 03 2016

Keywords

• nonn

Comments

From Antoine de Saint Germain, Dec 30 2024: (Start)

Sequence consists of integers, see Math StackExchange link.

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)

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..15
• Math StackExchange, Is A276175 integer-only?

Crossrefs

Cf. A051786, A101879, A276175.

Programs

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

Mathematica

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 *)

Ruby

def A276453(n)
  a = [1, 1, 2, 6]
  ary = [1]
  while ary.size < n + 1
    i = a[1..-1].inject(1){|s, i| s * (i + 1)}
    break if i % a[0] > 0
    a = *a[1..-1], i / a[0]
    ary << a[0]
  end
  ary
end

Formula

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