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A276258 a(n) = 4*a(n-1)*a(n-2) - a(n-3), with a(1) = a(2) = a(3) = 1. 3
1, 1, 1, 3, 11, 131, 5761, 3018753, 69564144001, 839987873581797251, 233732149587751710483796746251, 785328685279672432967483833110876164468741280003, 734226246973363127354668827312570246092792043625372932024478449584047744277761 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..18

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

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 *)

PROG

(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

CROSSREFS

Cf. A001519, A064098, A276256, A276259.

Sequence in context: A201611 A088075 A088076 * A284604 A072878 A112957

Adjacent sequences:  A276255 A276256 A276257 * A276259 A276260 A276261

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 25 2016

STATUS

approved

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Last modified February 25 09:44 EST 2020. Contains 332221 sequences. (Running on oeis4.)