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37, 146, 327, 580, 905, 1302, 1771, 2312, 2925, 3610, 4367, 5196, 6097, 7070, 8115, 9232, 10421, 11682, 13015, 14420, 15897, 17446, 19067, 20760, 22525, 24362, 26271, 28252, 30305, 32430, 34627, 36896, 39237, 41650, 44135, 46692, 49321, 52022
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (10368*n^2+288*n+1)^2-(36*n^2+n)*(1728*n+24)^2=1 can be written as A157326(n)^2-a(n)*A157325(n)^2=1.
This is the case s=6 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 26 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
| a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jan 26 2012
G.f.: x*(-37-35*x)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {37, 146, 327}, 50] (* Vincenzo Librandi, Jan 26 2012 *)
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PROG
| (MAGMA) I:=[37, 146, 327]; [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 26 2012
(PARI) for(n=1, 40, print1(36*n^2 + n", ")); \\ Vincenzo Librandi, Jan 26 2012
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CROSSREFS
| Cf. A157325, A157326.
Sequence in context: A142498 A158591 A031690 * A141968 A142656 A145898
Adjacent sequences: A157321 A157322 A157323 * A157325 A157326 A157327
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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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