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 A189356 a(n) gives y-values solving the Diophantine equation 2*x^2 + (x-1)^2 = y^2 for positive x. 2
 3, 41, 571, 7953, 110771, 1542841, 21489003, 299303201, 4168755811, 58063278153, 808717138331, 11263976658481, 156886956080403, 2185153408467161, 30435260762459851, 423908497265970753, 5904283700961130691, 82236063316189858921, 1145400602725696894203 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS (a(n)-1)/2 gives indices of triangular numbers which are also pentagonal (A046175). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 Index entries for linear recurrences with constant coefficients, signature (14,-1). FORMULA a(n) = 14*a(n-1) - a(n-2). G.f.: x*(3-x)/(1-14*x+x^2). - Bruno Berselli, May 03 2011 MATHEMATICA LinearRecurrence[{14, -1}, {3, 41}, 19]  (* Bruno Berselli, Nov 11 2011 *) PROG (MAGMA) [n le 2 select 38*n-35 else 14*Self(n-1)-Self(n-2): n in [1..19]]; // Bruno Berselli, May 03 2011 CROSSREFS Cf. A081065, A046174, A046175. Sequence in context: A087544 A305667 A213378 * A155672 A073844 A138961 Adjacent sequences:  A189353 A189354 A189355 * A189357 A189358 A189359 KEYWORD nonn AUTHOR Sture Sjöstedt, May 02 2011 EXTENSIONS Extended by T. D. Noe, May 02 2011 STATUS approved

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Last modified May 11 13:41 EDT 2021. Contains 343791 sequences. (Running on oeis4.)