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 A158447 a(n) = 10*n^2 - 1. 2
 9, 39, 89, 159, 249, 359, 489, 639, 809, 999, 1209, 1439, 1689, 1959, 2249, 2559, 2889, 3239, 3609, 3999, 4409, 4839, 5289, 5759, 6249, 6759, 7289, 7839, 8409, 8999, 9609, 10239, 10889, 11559, 12249, 12959, 13689, 14439, 15209, 15999, 16809, 17639 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The identity (10*n^2-1)^2-(25*n.^2-5) *(2*n)^2=1 can be written as a(n)^2-A158446(n)*A005843(n)^2=1. Sequence found by reading the line from 9, in the direction 9, 39,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Jul 18 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). G.f: x*(9+12*x-x^2)/(1-x)^3. a(n) = A033583(n) - 1. - Omar E. Pol, Jul 18 2012 MAPLE A158447:=n->10*n^2-1: seq(A158447(n), n=1..100); # Wesley Ivan Hurt, Apr 26 2017 MATHEMATICA Table[10n^2-1, {n, 50}] LinearRecurrence[{3, -3, 1}, {9, 39, 89}, 50] (* Harvey P. Dale, Dec 08 2017 *) PROG (MAGMA) I:=[9, 39, 89]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; (PARI) a(n) = 10*n^2 - 1. CROSSREFS Cf. A005843, A033583, A085787, A158446. Sequence in context: A050854 A053181 A192608 * A281381 A226449 A299280 Adjacent sequences:  A158444 A158445 A158446 * A158448 A158449 A158450 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Mar 19 2009 STATUS approved

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Last modified December 14 03:31 EST 2019. Contains 329978 sequences. (Running on oeis4.)