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A276095 A nonlinear recurrence of order 4: a(1)=a(2)=a(3)=a(4)=1; a(n)=(a(n-1)+a(n-2)+a(n-3))^2/a(n-4). 5
1, 1, 1, 1, 9, 121, 17161, 298978681, 9933176210033041, 815437979830770470704295274609, 38747106750801481775941360512378545527545442200632960401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

All terms are perfect squares.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..15

FORMULA

a(n) = A072878(n)^2.

a(n) = 16*a(n-1)*a(n-2)*a(n-3) - 2a(n-1) - 2a(n-2) - 2a(n-3) - a(n-4).

a(n)*a(n-1)*a(n-2)*a(n-3) = ((a(n) + a(n-1) + a(n-2) + a(n-3))/4)^2.

MATHEMATICA

RecurrenceTable[{a[n] == (a[n - 1] + a[n - 2] + a[n - 3])^2/a[n - 4], a[1] == a[2] == a[3] == a[4] == 1}, a, {n, 1, 12}] (* Michael De Vlieger, Aug 18 2016 *)

PROG

(Ruby)

def A(m, n)

  a = Array.new(m, 1)

  ary = [1]

  while ary.size < n

    i = a[1..-1].inject(:+)

    j = i * i

    break if j % a[0] > 0

    a = *a[1..-1], j / a[0]

    ary << a[0]

  end

  ary

end

def A276095(n)

  A(4, n)

end

CROSSREFS

Cf. A072878, A072882.

Sequence in context: A258380 A045976 A276256 * A053889 A295372 A293284

Adjacent sequences:  A276092 A276093 A276094 * A276096 A276097 A276098

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 18 2016

STATUS

approved

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Last modified June 19 11:24 EDT 2021. Contains 345127 sequences. (Running on oeis4.)