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A147529 Numbers n such that there exists x in N : (x+1)^3 - x^3 = 103*n^2.

%I A147529 #19 Jan 06 2024 00:59:09
%S A147529 8827,1133434915879903,145539221541371657392445143,
%T A147529 18688029378753350610679552570834161667,
%U A147529 2399644840493193509137754319007833077692312755187,308127477959355126566155341338642382333110448233345362623463
%N A147529 Numbers n such that there exists x in N : (x+1)^3 - x^3 = 103*n^2.
%H A147529 G. C. Greubel, <a href="/A147529/b147529.txt">Table of n, a(n) for n = 1..50</a>
%H A147529 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (128405450990,-1).
%F A147529 a(n+2) = 128405450990*a(n+1) - a(n).
%F A147529 G.f.: 8827*x*(1-x) / (1 - 128405450990*x + x^2). - _Colin Barker_, Oct 21 2014
%e A147529 a(1)=8827 because the first relation is (51721+1)^3 - 51721^3 = 103*8827^2.
%p A147529 seq(coeff(series(8827*x*(1-x)/(1-128405450990*x+x^2), x, n+1), x, n), n = 1..20); # _G. C. Greubel_, Jan 12 2020
%t A147529 LinearRecurrence[{128405450990,-1}, {8827,1133434915879903}, 20] (* _G. C. Greubel_, Jan 12 2020 *)
%o A147529 (PARI) Vec(8827*x*(1-x)/(1-128405450990*x+x^2) + O(x^20)) \\ _Colin Barker_, Oct 21 2014
%o A147529 (Magma) I:=[8827,1133434915879903]; [n le 2 select I[n] else 128405450990*Self(n-1) - Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 12 2020
%o A147529 (Sage)
%o A147529 def A147529_list(prec):
%o A147529     P.<x> = PowerSeriesRing(ZZ, prec)
%o A147529     return P( 8827*x*(1-x)/(1-128405450990*x+x^2) ).list()
%o A147529 a=A147529_list(20); a[1:] # _G. C. Greubel_, Jan 12 2020
%o A147529 (GAP) a:=[8827,1133434915879903];; for n in [3..20] do a[n]:=128405450990*a[n-1]+3*a[n-2]-a[n-3]; od; a; # _G. C. Greubel_, Jan 12 2020
%Y A147529 Cf. A147527, A147528, A147530.
%K A147529 easy,nonn
%O A147529 1,1
%A A147529 _Richard Choulet_, Nov 06 2008
%E A147529 Editing and a(6) from _Colin Barker_, Oct 21 2014