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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.)