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 A077241 Combined Diophantine Chebyshev sequences A054488 and A077413. 14
 1, 2, 8, 13, 47, 76, 274, 443, 1597, 2582, 9308, 15049, 54251, 87712, 316198, 511223, 1842937, 2979626, 10741424, 17366533, 62605607, 101219572, 364892218, 589950899, 2126747701, 3438485822, 12395593988, 20040964033, 72246816227, 116807298376 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS -8*a(n)^2 + b(n)^2 = 17, with the companion sequence b(n)= A077242(n). The number a > 0 belongs to the sequence A077241, if a^2 belongs to the sequence A034856. - Alzhekeyev Ascar M, Apr 27 2012 Numbers k such that k^2 + 2 is a triangular number (see A214838). - Alex Ratushnyak, Mar 07 2013 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1). FORMULA a(2k) = A054488(k) and a(2k+1)= A077413(k) for k>=0. G.f.: (1+x)*(1+x+x^2)/(1-6*x^2+x^4). a(n) = (-1)^n*((4-5*sqrt(2))*(1-(-1)^n*sqrt(2))^(2*floor((n+1)/2))+(4+5*sqrt(2))*(1+(-1)^n*sqrt(2))^(2*floor((n+1)/2)))/8. [Bruno Berselli, Mar 10 2013] EXAMPLE 8*a(2)^2 + 17 = 8*8^2+17 = 529 = 23^2 = A077242(2)^2. MATHEMATICA LinearRecurrence[{0, 6, 0, -1}, {1, 2, 8, 13}, 30] (* Bruno Berselli, Mar 10 2013 *) CoefficientList[Series[(1 + x) (1 + x + x^2)/(1 - 6 x^2 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 18 2014 *) PROG (Maxima) makelist(expand((-1)^n*((4-5*sqrt(2))*(1-(-1)^n*sqrt(2))^(2*floor((n+1)/2))+(4+5*sqrt(2))*(1+(-1)^n*sqrt(2))^(2*floor((n+1)/2)))/8), n, 0, 30); /* Bruno Berselli, Mar 10 2013 */ (MAGMA) I:=[1, 2, 8, 13]; [n le 4 select I[n] else 6*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Feb 18 2014 CROSSREFS Sequence in context: A095825 A106359 A257036 * A228469 A066567 A329453 Adjacent sequences:  A077238 A077239 A077240 * A077242 A077243 A077244 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Nov 08 2002 STATUS approved

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Last modified April 22 13:51 EDT 2021. Contains 343177 sequences. (Running on oeis4.)