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 A147530 Numbers x such that there exists n in N : (x+1)^3 - x^3 = 103*n^2. 5
 51721, 6641322533431006, 852782015075257741682069713, 109501859241899449111168441436054160358, 14060635620199598267351285586436862449157290510201, 1805462258017787769335954916623470050495526664967434749114126 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Colin Barker, Table of n, a(n) for n = 1..90 Index entries for linear recurrences with constant coefficients, signature (128405450991,-128405450991,1). FORMULA a(n+2) = 128405450990*a(n+1) - a(n) + 62402725494. G.f.: x*(51721 + 64202725495*x - 51722*x^2)/((1-x)*(1 - 128405450990*x + x^2)). - Colin Barker, Oct 21 2014, corrected Jul 13 2016 EXAMPLE a(1)=51721 because the first relation is : 51722^3 - 51721^3 = 103*8827^2. MAPLE seq(coeff(series(x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x + x^2)), x, n+1), x, n), n = 1..20); # G. C. Greubel, Jan 12 2020 MATHEMATICA LinearRecurrence[{128405450991, -128405450991, 1}, {51721, 6641322533431006, 852782015075257741682069713}, 20] (* G. C. Greubel, Jan 12 2020 *) PROG (PARI) Vec(x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x+x^2)) + O(x^10)) \\ Colin Barker, Oct 21 2014, corrected Jul 13 2016 (PARI) isok(x) = issquare(((x+1)^3-x^3)/103) \\ Colin Barker, Jul 13 2016 (MAGMA) I:=[51721, 6641322533431006]; [n le 2 select I[n] else 128405450990*Self(n-1) - Self(n-2) + 62402725494: n in [1..20]]; // G. C. Greubel, Jan 12 2020 (Sage) def A147530_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x + x^2)) ).list() a=A147530_list(20); a[1:] # G. C. Greubel, Jan 12 2020 (GAP) a:=[51721, 6641322533431006];; for n in [3..20] do a[n]:=128405450990*a[n-1] -a[n-2] +62402725494; od; a; # G. C. Greubel, Jan 12 2020 CROSSREFS Cf. A147527, A147528, A147529. Sequence in context: A344645 A203354 A289823 * A184454 A003134 A253989 Adjacent sequences:  A147527 A147528 A147529 * A147531 A147532 A147533 KEYWORD nonn,easy AUTHOR Richard Choulet, Nov 06 2008 EXTENSIONS Editing and a(6) from Colin Barker, Oct 21 2014 a(3) to a(6) corrected by Colin Barker, Jul 13 2016 STATUS approved

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Last modified January 29 05:09 EST 2022. Contains 350672 sequences. (Running on oeis4.)