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80, 322, 726, 1292, 2020, 2910, 3962, 5176, 6552, 8090, 9790, 11652, 13676, 15862, 18210, 20720, 23392, 26226, 29222, 32380, 35700, 39182, 42826, 46632, 50600, 54730, 59022, 63476, 68092, 72870, 77810, 82912, 88176, 93602, 99190, 104940
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (162*n-1)^2-(81*n^2-n)*(18)^2=1 can be written as A157954(n)^2-a(n)*(16)^2=1. - 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
E. J. Barbeau, Polynomial Excursions, Chapter 10:Diophantine equations (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(9^2*t-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 29 2012
G.f.: x*(-80-82*x)/(x-1)^3. - Vincenzo Librandi, Jan 29 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {80, 322, 726}, 50] (* Vincenzo Librandi, Jan 29 2012 *)
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PROG
| (MAGMA) I:=[80, 322, 726]; [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(81*n^2 - n", ")); \\ Vincenzo Librandi, Jan 29 2012
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CROSSREFS
| Cf. A157954.
Sequence in context: A057441 A204483 A204475 * A045666 A045657 A085774
Adjacent sequences: A157950 A157951 A157952 * A157954 A157955 A157956
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009
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