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Search: id:A158537
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| 1, 23, 89, 199, 353, 551, 793, 1079, 1409, 1783, 2201, 2663, 3169, 3719, 4313, 4951, 5633, 6359, 7129, 7943, 8801, 9703, 10649, 11639, 12673, 13751, 14873, 16039, 17249, 18503, 19801, 21143, 22529, 23959, 25433, 26951, 28513, 30119, 31769
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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From the Pell-type identity (22*n^2+1)^2 - (121*n^2+11) * (2*n)^2 = 1 we derive
(a(n))^2 - A158536(n) * (A005843(n))^2 = 1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
Edward Everett Withford, Pell Equation
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FORMULA
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a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: (1+20*x+23*x^2)/(1-x)^3.
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CROSSREFS
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Cf. A005843, A158536
Adjacent sequences: A158534 A158535 A158536 this_sequence A158538 A158539 A158540
Sequence in context: A044591 A050255 A014088 this_sequence A117049 A142062 A050529
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KEYWORD
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nonn,easy,new
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 21 2009
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EXTENSIONS
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Comment rewritten, a(0) added - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2009
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