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A154515
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648n^2 + 72n + 1.
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3
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721, 2737, 6049, 10657, 16561, 23761, 32257, 42049, 53137, 65521, 79201, 94177, 110449, 128017, 146881, 167041, 188497, 211249, 235297, 260641, 287281, 315217, 344449, 374977, 406801, 439921, 474337, 510049, 547057, 585361, 624961, 665857
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (648*n^2+72*n+1)^2-(9*n^2+n)*(216*n+12)^2=1 can be written as a(n)^2-A154517(n)*A154519(n)^2=1. This is the case s=3 of the identity (8*n^2*s^4+8*n*s^2+1)^2 - (n^2*s^2+n)*(8*n*s^3+4*s)^2 = 1. - Vincenzo Librandi, Jan 30 2012
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: x*(721+574*x+x^2)/(1-x)^3. a(1)=721, a(2)=2737, a(3)=6049, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Colin Barker, Jan 25 2012
a(n) = 2*A161705(n)^2-1. - Bruno Berselli, Jan 31 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {721, 2737, 6049}, 50] (* Vincenzo Librandi, Jan 30 2012 *)
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PROG
| (PARI) a(n)=648*n^2+72*n+1 \\ Charles R Greathouse IV, Dec 27 2011
(MAGMA) I:=[721, 2737, 6049]; [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 30 2012
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CROSSREFS
| Cf. A154517, A154519.
Sequence in context: A034179 A014440 A159295 * A053497 A139154 A139165
Adjacent sequences: A154512 A154513 A154514 * A154516 A154517 A154518
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 11 2009
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