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27, 756, 2943, 6588, 11691, 18252, 26271, 35748, 46683, 59076, 72927, 88236, 105003, 123228, 142911, 164052, 186651, 210708, 236223, 263196, 291627, 321516, 352863, 385668, 419931, 455652, 492831, 531468, 571563, 613116, 656127, 700596, 746523
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The identity (54*n^2+1)^2-(729*n^2+27)*(2*n)^2 = 1 can be written as A158646(n)^2-a(n)*A005843(n)^2 =1.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..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.: -27*(1+25*x+28*x^2)/(x-1)^3.
a(n)= 3*a(n-1) -3*a(n-2) +a(n-3).
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {27, 756, 2943}, 50] (* Vincenzo Librandi, Feb 17 2012 *)
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PROG
| (MAGMA) I:=[27, 756, 2943]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 17 2012
(PARI) for(n=0, 40, print1(729*n^2 + 27", ")); \\ Vincenzo Librandi, Feb 17 2012
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CROSSREFS
| Cf. A005843, A158646.
Sequence in context: A046240 A042406 A159668 * A138979 A183505 A159234
Adjacent sequences: A158642 A158643 A158644 * A158646 A158647 A158648
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 23 2009
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EXTENSIONS
| Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009
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