A276258 a(n) = 4*a(n-1)*a(n-2) - a(n-3), with a(1) = a(2) = a(3) = 1.
1, 1, 1, 3, 11, 131, 5761, 3018753, 69564144001, 839987873581797251, 233732149587751710483796746251, 785328685279672432967483833110876164468741280003, 734226246973363127354668827312570246092792043625372932024478449584047744277761
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..18
Programs
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Mathematica
RecurrenceTable[{a[n] == 4*a[n - 1]*a[n - 2] - a[n - 3], a[1] == 1, a[2] == 1, a[3] == 1}, a, {n, 1, 10}] (* G. C. Greubel, Aug 25 2016 *) -
Ruby
def A(m, n) a = Array.new(m, 1) ary = [1] while ary.size < n a = *a[1..-1], *a[1..-1].inject(:*) * (m + 1) - a[0] ary << a[0] end ary end def A276258(n) A(3, n) end
Formula
a(1)=a(2)=a(3)=1; a(n)=(a(n-1)^2+a(n-2)^2+1)/a(n-3).
a(n) ~ 1/4 * c^(((1+sqrt(5))/2)^n), where c = 1.41452525081158447693692520473959... . - Vaclav Kotesovec, Aug 26 2016
a(n)*a(n+1)*a(n+2) = (a(n)^2+a(n+1)^2+a(n+2)^2+1)/4. - Seiichi Manyama, Sep 04 2016
Comments