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A147528
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Numbers x such that (x + 103)^3 - x^3 is a square.
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4
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5327263, 684056220943393618, 87836547552751547393253180439, 11278691501915643258450349467913578516874, 1448245468880558621537182415402996832263200922550703, 185962612575832140241603356412217415201039246491645779158754978
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n+2) = 128405450990*a(n+1) - a(n) + 6612880725882.
G.f.: 103*x*(51721 + 64202725495*x - 51722*x^2) / ((1-x)*(1 -128405450990*x +x^2)). - Colin Barker, Oct 21 2014
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EXAMPLE
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a(1) = 5327263 because the first relation is : (5327263 + 103)^3 - 5327263^3 = 93645643^2.
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MAPLE
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seq(coeff(series(103*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 10 2020
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MATHEMATICA
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LinearRecurrence[{128405450991, -128405450991, 1}, {5327263, 684056220943393618, 87836547552751547393253180439}, 20] (* G. C. Greubel, Jan 10 2020 *)
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PROG
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(PARI) Vec(103*x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x+x^2)) + O(x^20)) \\ Colin Barker, Oct 21 2014
(Magma) I:=[5327263, 684056220943393618, 87836547552751547393253180439]; [n le 3 select I[n] else 128405450991*Self(n-1) - 128405450991*Self(n-2) + Self(n-3): n in [1..20]]; // G. C. Greubel, Jan 10 2020
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 103*x*(51721 + 64202725495*x - 51722*x^2) / ((1-x)*(1 -128405450990*x +x^2)) ).list()
(GAP) a:=[5327263, 684056220943393618, 87836547552751547393253180439];; for n in [4..20] do a[n]:=128405450991*a[n-1] - 128405450991*a[n-2] + a[n-3]; od; a; # G. C. Greubel, Jan 10 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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