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Search: id:A158591
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| 1, 37, 145, 325, 577, 901, 1297, 1765, 2305, 2917, 3601, 4357, 5185, 6085, 7057, 8101, 9217, 10405, 11665, 12997, 14401, 15877, 17425, 19045, 20737, 22501, 24337, 26245, 28225, 30277, 32401, 34597, 36865, 39205, 41617, 44101, 46657, 49285, 51985
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The identity (36*n^2+1)^2 - (324*n^2+18)*(2*n)^2 = 1 can be written in
Pell-format as (a(n))^2 - A158590(n)* (A005843(n))^2 =1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
Wolfram MathWorld, 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+34*x+37*x^2)/(x-1)^3.
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CROSSREFS
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Cf. A005843, A158590
Adjacent sequences: A158588 A158589 A158590 this_sequence A158592 A158593 A158594
Sequence in context: A044750 A141936 A142498 this_sequence A031690 A157324 A141968
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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 22 2009
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EXTENSIONS
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Comment rewritten, formula replaced by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2009
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