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A113848
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a(1) = a(2) = 1, a(n+2) = 2*a(n) + a(n+1)^2.
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1
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1, 1, 3, 11, 127, 16151, 260855055, 68045359719085327, 4630170979299719971778494028407039, 21438483297549327871400796194793048411084076762817293736211302918175
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| In this sequence the primes begin a(3) = 3, a(4) = 11, a(5) = 127, a(9) = 4630170979299719971778494028407039.
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LINKS
| Index entries for sequences of form a(n+1)=a(n)^2 + ...
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FORMULA
| a(1) = a(2) = 1, for n>2: a(n) = 2*a(n-2) + a(n-1)^2. a(1) = a(2) = 1, for n>0: a(n+2) = 2*a(n) + a(n+1)^2.
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EXAMPLE
| a(1) = 1 by definition.
a(2) = 1 by definition.
a(3) = 2*1 + 1^2 = 3.
a(4) = 2*1 + 3^2 = 11.
a(5) = 2*3 + 11^2 = 127.
a(6) = 2*11 + 127^2 = 16151.
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MATHEMATICA
| Join[{a=1, b=1}, Table[c=1*b^2+2*a; a=b; b=c, {n, 10}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 18 2011*)
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CROSSREFS
| Cf. A000278, A000283, A014253, A063827, A072878, A112957, A112958, A112959, A112960, A112961, A112969, A113785.
Sequence in context: A015047 A102847 A113258 * A201611 A088075 A088076
Adjacent sequences: A113845 A113846 A113847 * A113849 A113850 A113851
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 24 2006
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