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A157337
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128n^2 + 32n + 1.
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2
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161, 577, 1249, 2177, 3361, 4801, 6497, 8449, 10657, 13121, 15841, 18817, 22049, 25537, 29281, 33281, 37537, 42049, 46817, 51841, 57121, 62657, 68449, 74497, 80801, 87361, 94177, 101249, 108577, 116161, 124001, 132097, 140449, 149057
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (128*n^2+32*n+1)^2-(4*n^2+n)*(64*n+8)^2=1 can be written as a(n)^2-A007742(n)*A157336(n)^2=1 (see also second part of the comment in A157336). - Vincenzo Librandi, Jan 29 2012
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: x*(-x^2-94*x-161)/(x-1)^3. - Vincenzo Librandi, Jan 29 2012
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jan 29 2012
a(n) = 2*A017077(n)^2-1. - Bruno Berselli, Jan 29 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {161, 577, 1249}, 50] (* Vincenzo Librandi, Jan 29 2012 *)
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PROG
| (MAGMA) I:=[161, 577, 1249]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
(PARI) for(n=1, 40, print1(128*n^2 + 32*n + 1", ")); \\ Vincenzo Librandi, Jan 29 2012
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CROSSREFS
| Cf. A007742, A157336.
Sequence in context: A060641 A157954 A159545 * A200869 A200883 A196635
Adjacent sequences: A157334 A157335 A157336 * A157338 A157339 A157340
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 27 2009
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