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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. 2
1, 1, 1, 1, 1, 2, 4, 12, 108, 10584, 27454896, 94148851006224, 246222177535609206635748240, 62371770277951054762478578990896212287188931341600, 3750595553941161278345366267513070968239986992860645038477600300348697171928615364721752014400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Inspired by Somos-5 sequence.

a(n) is integer for n >= 0.

a(n+1)/a(n) is integer for n >= 0.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..17

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.

EXAMPLE

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.

PROG

(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

CROSSREFS

Cf. A006721, A276535.

Sequence in context: A038791 A326950 A001696 * A326969 A304986 A013333

Adjacent sequences:  A276531 A276532 A276533 * A276535 A276536 A276537

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 16 2016

STATUS

approved

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)