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 A158493 a(n) = 20*n^2 + 1. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Vincenzo Librandi, X^2-AY^2=1 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From Vincenzo Librandi, Feb 21 2012: (Start) G.f.: -(1 + 18*x + 21*x^2)/(x-1)^3; a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End) MATHEMATICA LinearRecurrence[{3, -3, 1}, {1, 21, 81}, 50] (* Vincenzo Librandi, Feb 21 2012 PROG (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 CROSSREFS Cf. A005843, A158492. Sequence in context: A296970 A068085 A135945 * A159743 A219593 A195961 Adjacent sequences:  A158490 A158491 A158492 * A158494 A158495 A158496 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Mar 21 2009 EXTENSIONS Edited by N. J. A. Sloane, Oct 12 2009 STATUS approved

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Last modified December 14 07:03 EST 2019. Contains 329978 sequences. (Running on oeis4.)