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A147530 Numbers x such that there exists n in N : (x+1)^3 - x^3 = 103*n^2.

%I A147530 #26 Sep 08 2022 08:45:38
%S A147530 51721,6641322533431006,852782015075257741682069713,
%T A147530 109501859241899449111168441436054160358,
%U A147530 14060635620199598267351285586436862449157290510201,1805462258017787769335954916623470050495526664967434749114126
%N A147530 Numbers x such that there exists n in N : (x+1)^3 - x^3 = 103*n^2.
%H A147530 Colin Barker, <a href="/A147530/b147530.txt">Table of n, a(n) for n = 1..90</a>
%H A147530 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (128405450991,-128405450991,1).
%F A147530 a(n+2) = 128405450990*a(n+1) - a(n) + 62402725494.
%F A147530 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
%e A147530 a(1)=51721 because the first relation is : 51722^3 - 51721^3 = 103*8827^2.
%p A147530 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
%t A147530 LinearRecurrence[{128405450991,-128405450991,1}, {51721, 6641322533431006, 852782015075257741682069713}, 20] (* _G. C. Greubel_, Jan 12 2020 *)
%o A147530 (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
%o A147530 (PARI) isok(x) = issquare(((x+1)^3-x^3)/103) \\ _Colin Barker_, Jul 13 2016
%o A147530 (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
%o A147530 (Sage)
%o A147530 def A147530_list(prec):
%o A147530     P.<x> = PowerSeriesRing(ZZ, prec)
%o A147530     return P( x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x + x^2)) ).list()
%o A147530 a=A147530_list(20); a[1:] # _G. C. Greubel_, Jan 12 2020
%o A147530 (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
%Y A147530 Cf. A147527, A147528, A147529.
%K A147530 nonn,easy
%O A147530 1,1
%A A147530 _Richard Choulet_, Nov 06 2008
%E A147530 Editing and a(6) from _Colin Barker_, Oct 21 2014
%E A147530 a(3) to a(6) corrected by _Colin Barker_, Jul 13 2016