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A157664
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80000n^2 + 800n + 1.
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3
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80801, 321601, 722401, 1283201, 2004001, 2884801, 3925601, 5126401, 6487201, 8008001, 9688801, 11529601, 13530401, 15691201, 18012001, 20492801, 23133601, 25934401, 28895201, 32016001, 35296801, 38737601, 42338401, 46099201
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity (80000n^2+800n+1)^2-(100n^2+n)*(8000n+40)^2=1 can be written as a(n)^2-A055438(n)*A157663(n)^2=1. - Vincenzo Librandi, Feb 04 2012
This is the case s=10 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. - Bruno Berselli, Feb 04 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
| G.f.: x*(80801+79198*x+x^2)/(1-x)^3. - Vincenzo Librandi, Feb 04 2012
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Vincenzo Librandi, Feb 04 2012
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {80801, 321601, 722401}, 50] (* Vincenzo Librandi, Feb 04 2012 *)
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PROG
| (MAGMA) I:=[80801, 321601, 722401]; [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, Feb 04 2012
(PARI) for(n=1, 40, print1(80000*n^2 + 800*n + 1", ")); \\ Vincenzo Librandi, Feb 04 2012
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CROSSREFS
| Cf. A055438, A157663.
Sequence in context: A095946 A050517 A069304 * A064001 A029752 A043608
Adjacent sequences: A157661 A157662 A157663 * A157665 A157666 A157667
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 04 2009
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