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1, 21, 81, 181, 321, 501, 721, 981, 1281, 1621, 2001, 2421, 2881, 3381, 3921, 4501, 5121, 5781, 6481, 7221, 8001, 8821, 9681, 10581, 11521, 12501, 13521, 14581, 15681, 16821, 18001, 19221, 20481, 21781, 23121, 24501, 25921, 27381, 28881, 30421
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OFFSET
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0,2
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COMMENTS
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The identity (20*n^2+1)^2-(100*n^2+10)*(2*n)^2 = 1 can be written as a(n)^2-A158492(n)*A005843(n)^2 = 1. - Vincenzo Librandi, Feb 21 2012
Sequence found by reading the segment (1, 21) together with the line from 21, in the direction 21, 81,..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. - Omar E. Pol, Nov 05 2012
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LINKS
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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
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G.f.: -(1+18*x+21*x^2)/(x-1)^3. - Vincenzo Librandi, Feb 21 2012
a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Feb 21 2012
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1, 21, 81}, 50] (* Vincenzo Librandi, Feb 21 2012
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PROG
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(MAGMA) I:=[1, 21, 81]; [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 21 2012
(PARI) for(n=0, 40, print1(20*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 21 2012
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CROSSREFS
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Cf. A005843, A158492.
Sequence in context: A172082 A068085 A135945 * A159743 A219593 A195961
Adjacent sequences: A158490 A158491 A158492 * A158494 A158495 A158496
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 21 2009
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EXTENSIONS
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Edited by N. J. A. Sloane, Oct 12 2009
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STATUS
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approved
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