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A157863
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103680000n^2 + 28800n + 1.
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3
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103708801, 414777601, 933206401, 1658995201, 2592144001, 3732652801, 5080521601, 6635750401, 8398339201, 10368288001, 12545596801, 14930265601, 17522294401, 20321683201, 23328432001, 26542540801, 29964009601, 33592838401
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (103680000*n^2+28800*n+1)^2-(3600*n^2+n)*(1728000*n+240)^2=1 can be written as a(n)^2-A157861(n)*A157862(n)^2=1. - Vincenzo Librandi, Jan 25 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 25 2012
G.f.: x*(-x^2-103651198*x-103708801)/(x-1)^3. - Vincenzo Librandi, Jan 25 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {103708801, 414777601, 933206401}, 40] (* Vincenzo Librandi, Jan 25 2012 *)
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PROG
| (MAGMA) I:=[103708801, 414777601, 933206401]; [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, Jan 25 2012
(PARI) for(n=1, 22, print1(103680000*n^2 + 28800*n + 1", ")); \\ Vincenzo Librandi, Jan 25 2012
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CROSSREFS
| Cf. A157861, A157862.
Sequence in context: A112717 A114679 A157859 * A035498 A018897 A124149
Adjacent sequences: A157860 A157861 A157862 * A157864 A157865 A157866
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 08 2009
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