A276284 a(0) = a(1) = a(2) = a(3) = a(4) = 1; for n > 4, a(n) = ( a(n-1)+a(n-3)+1 )*( a(n-2)+a(n-4)+1 ) / a(n-5).

1, 1, 1, 1, 1, 9, 33, 385, 13825, 5474305, 8430415841, 1398605982547209, 30625582893143965429313, 3098236789946633955987434183345281, 17332850039068891068793031113694107707268123637761

Offset: 0

Author

Seiichi Manyama, Aug 27 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..21

Crossrefs

Cf. A276123.

Programs

Mathematica

RecurrenceTable[{a[n] == (a[n - 1] + a[n - 3] + 1) (a[n - 2] + a[n - 4] + 1)/a[n - 5], a[0] == a[1] == a[2] == a[3] == a[4] == 1}, a, {n, 0, 14}] (* Michael De Vlieger, Aug 27 2016 *)
nxt[{a_,b_,c_,d_,e_}]:={b,c,d,e,(e+c+1) (d+b+1)/a}; NestList[nxt,{1,1,1,1,1},15][[All,1]] (* Harvey P. Dale, Dec 14 2021 *)

Ruby

def A(m, n)
  a = Array.new(2 * m + 1, 1)
  ary = [1]
  while ary.size < n + 1
    i = (1..m).inject(1){|s, i| s + a[2 * i - 1]} * (1..m).inject(1){|s, i| s + a[2 * i]}
    break if i % a[0] > 0
    a = *a[1..-1], i / a[0]
    ary << a[0]
  end
  ary
end
def A276284(n)
  A(2, n)
end

Formula

a(n) = (8-4*(-1)^n)*a(n-1)*a(n-3) - a(n-2) - a(n-4) - 1 for n>3.