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 A042300 Numerators of continued fraction convergents to sqrt(677). 2
 26, 1353, 70382, 3661217, 190453666, 9907251849, 515367549814, 26809019842177, 1394584399343018, 72545197785679113, 3773744869254656894, 196307278399027837601, 10211752221618702212146, 531207422802571542869193, 27632997737955338931410182 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (52, 1). FORMULA a(n) = 52*a(n-1)+a(n-2) for n>1, a(0)=26, a(1)=1353. G.f.: (26+x)/(1-52*x -x^2). [Philippe Deléham, Nov 23 2008] a(n) = 13*((26+sqrt(677))^n+(26-sqrt(677))^n)+(1/2)*sqrt(677)*((26+sqrt(677))^n-(26-sqrt(677))^n). [Paolo P. Lava, Nov 28 2008] MATHEMATICA Numerator[Convergents[Sqrt[677], 30]] (* or *) LinearRecurrence[{52, 1}, {26, 1353}, 30] (* Harvey P. Dale, Nov 09 2011 *) PROG (MAGMA) I:=[26, 1353]; [n le 2 select I[n] else 52*Self(n-1)+Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013 CROSSREFS Cf. A042301, A040650. Sequence in context: A106710 A114052 A042303 * A282884 A080163 A217228 Adjacent sequences:  A042297 A042298 A042299 * A042301 A042302 A042303 KEYWORD nonn,cofr,frac,easy AUTHOR EXTENSIONS Additional term from Colin Barker, Dec 07 2013 STATUS approved

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