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Search: id:A158740
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| 1, 73, 289, 649, 1153, 1801, 2593, 3529, 4609, 5833, 7201, 8713, 10369, 12169, 14113, 16201, 18433, 20809, 23329, 25993, 28801, 31753, 34849, 38089, 41473, 45001, 48673, 52489, 56449, 60553, 64801, 69193, 73729, 78409, 83233, 88201, 93313
(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 (72*n^2+1)^2 - (1296*n^2+36) * (2*n)^2 = 1 can be written as
the Pell equation (a(n))^2 - A158739(n) * (A005843(n))^2 = 1.
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LINKS
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Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
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+70*x+73*x^2)/(x-1)^3.
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CROSSREFS
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Cf. A158739, A005843
Sequence in context: A142489 A033244 A140857 this_sequence A142614 A158744 A142406
Adjacent sequences: A158737 A158738 A158739 this_sequence A158741 A158742 A158743
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 25 2009
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EXTENSIONS
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Comment rewritten, a(0) added and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009
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