A276534 a(n) = a(n-1) * a(n-4) * (a(n-2) * a(n-3) + 1) / a(n-5), with a(0) = a(1) = a(2) = a(3) = a(4) = 1.
1, 1, 1, 1, 1, 2, 4, 12, 108, 10584, 27454896, 94148851006224, 246222177535609206635748240, 62371770277951054762478578990896212287188931341600, 3750595553941161278345366267513070968239986992860645038477600300348697171928615364721752014400
Offset: 0
Keywords
Examples
a(5) = a(4) * b(4) = 1 * 2 = 2, a(6) = a(5) * b(5) = 2 * 2 = 4, a(7) = a(6) * b(6) = 4 * 3 = 12, a(8) = a(7) * b(7) = 12 * 9 = 108.
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..17
Programs
-
Ruby
def A(k, n) a = Array.new(2 * k + 1, 1) ary = [1] while ary.size < n + 1 i = 0 k.downto(1){|j| i += 1 i *= a[j] * a[-j] } break if i % a[0] > 0 a = *a[1..-1], i / a[0] ary << a[0] end ary end def A276534(n) A(2, n) end
Formula
a(n) * a(n-5) = a(n-1) * a(n-4) + a(n-1) * a(n-2) * a(n-3) * a(n-4).
a(4-n) = a(n).
Let b(n) = b(n-4) * (b(n-2) * (b(0) * b(1) * ... * b(n-3))^2 + 1) with b(0) = b(1) = b(2) = b(3) = 1, then a(n) = a(n-1) * b(n-1) = b(0) * b(1) * ... * b(n-1) for n > 0.
Comments