A276416 a(n) = a(n-1)*(1 + a(n-1)/a(n-4)), with a(0) = a(1) = a(2) = a(3) = 1.

1, 1, 1, 1, 2, 6, 42, 1806, 1632624, 444245153520, 4698898962968253924720, 12225720633546031105793020748137513851120, 91550929674875028299231929179221527919681972461210779957660001348767546720

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..16

Formula

0 = a(n)*(a(n+3) - a(n+4)) + a(n+3)*a(n+3) for all n>=0.

A133400(n) = a(n+1)/a(n).

Mathematica

RecurrenceTable[{a[n] == a[n - 1] (1 + a[n - 1]/a[n - 4]), a[0] == a[1] == a[2] == a[3] == 1}, a, {n, 0, 12}] (* Michael De Vlieger, Sep 04 2016 *)

Prog

(Ruby)
def A(m, n)
  a = Array.new(m, 1)
  ary = [1]
  while ary.size < n + 1
    break if a[-1] % a[0] > 0
    a = *a[1..-1], a[-1] * (1 + a[-1] / a[0])
    ary << a[0]
  end
  ary
end
def A276416(n)
  A(4, n)
end

Crossrefs

Cf. A133400, A250309.

Sequence in context: A349193 A230311 A379686 * A007018 A100016 A344562

Adjacent sequences: A276413 A276414 A276415 * A276417 A276418 A276419

Keyword

nonn

Author

Seiichi Manyama, Sep 02 2016

Status

approved