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 A157324 a(n) = 36*n^2 + n. 3
 37, 146, 327, 580, 905, 1302, 1771, 2312, 2925, 3610, 4367, 5196, 6097, 7070, 8115, 9232, 10421, 11682, 13015, 14420, 15897, 17446, 19067, 20760, 22525, 24362, 26271, 28252, 30305, 32430, 34627, 36896, 39237, 41650, 44135, 46692, 49321, 52022 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The identity (10368*n^2 + 288*n + 1)^2 - (36*n^2 + n)*(1728*n + 24)^2 = 1 can be written as A157326(n)^2 - a(n)*A157325(n)^2 = 1. This is the case s=6 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. - Vincenzo Librandi, Jan 26 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..10000 Vincenzo Librandi, X^2-AY^2=1 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012 G.f.: x*(-37 - 35*x)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012 MATHEMATICA LinearRecurrence[{3, -3, 1}, {37, 146, 327}, 50] (* Vincenzo Librandi, Jan 26 2012 *) Table[36n^2+n, {n, 50}] (* Harvey P. Dale, Mar 09 2019 *) PROG (Magma) I:=[37, 146, 327]; [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 26 2012 (PARI) for(n=1, 40, print1(36*n^2 + n", ")); \\ Vincenzo Librandi, Jan 26 2012 CROSSREFS Cf. A157325, A157326. Sequence in context: A262318 A262921 A031690 * A251113 A251106 A141968 Adjacent sequences: A157321 A157322 A157323 * A157325 A157326 A157327 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Feb 27 2009 STATUS approved

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Last modified September 16 20:53 EDT 2024. Contains 375977 sequences. (Running on oeis4.)