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Search: id:A113848
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| A113848 |
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A quadratic pseudofibonacci sequence. a(1) = a(2) = 1, a(n+2) = 2*a(n) + a(n+1)^2. |
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+0
2
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| 1, 1, 3, 11, 127, 16151, 260855055, 68045359719085327, 4630170979299719971778494028407039, 21438483297549327871400796194793048411084076762817293736211302918175
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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In this sequence the primes begin a(3) = 3, a(4) = 11, a(5) = 127, a(9) = 4630170979299719971778494028407039.
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FORMULA
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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
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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.
a(7) = 2*127 + 16151^2 = 260855055.
a(8) = 2*16151 + 260855055^2 = 68045359719085327.
a(9) = 2*260855055 + 68045359719085327^2 = 4630170979299719971778494028407039.
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CROSSREFS
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Cf. A000278, A000283, A014253, A063827, A072878, A112957, A112958, A112959, A112960, A112961, A112969, A113785.
Sequence in context: A015047 A102847 A113258 this_sequence A088075 A088076 A072878
Adjacent sequences: A113845 A113846 A113847 this_sequence A113849 A113850 A113851
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 24 2006
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