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