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A147527
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Numbers k such that there exists x in N : (x + 103)^3 - x^3 = k^2.
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4
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93645643, 12024611022569890927, 1544025601332411913276450522087, 198261303679194296628699373223979621125203, 25457832112792289938442435570354101121237746019778883, 3268924413670798537740342016261657034171968745307560952072318967
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OFFSET
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1,1
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..50
Index entries for linear recurrences with constant coefficients, signature (128405450990,-1).
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FORMULA
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a(n+2) = 128405450990*a(n+1) - a(n).
a(n) = (93645643/2)*( (64202725495 + 3652365444*sqrt(309))^n + (64202725495 - 3652365444*sqrt(309))^n ) - (10654629*sqrt(309)/4)*( (64202725495 - 3652365444*sqrt(309))^n - (64202725495 + 3652365444*sqrt(309))^n ) with n >= 0. - Paolo P. Lava, Nov 25 2008
G.f.: 93645643*x*(1-x)/(1 - 128405450990*x + x^2). - Colin Barker, Oct 21 2014
a(n) = sqrt(A147528(n) + 103)^3 - A147528(n)^3). - Michel Marcus, Jan 10 2020
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EXAMPLE
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a(1)=93645643 because the first relation is (5327263 + 103)^3 - 5327263^3 = 93645643^2.
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MAPLE
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seq(coeff(series(93645643*x*(1-x)/(1 - 128405450990*x + x^2), x, n+1), x, n), n = 0..20); # G. C. Greubel, Jan 10 2020
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MATHEMATICA
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LinearRecurrence[{128405450990, -1}, {93645643, 12024611022569890927}, 20] (* G. C. Greubel, Jan 10 2020 *)
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PROG
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(PARI) Vec(93645643*x*(1-x)/(1-128405450990*x+x^2) + O(x^20)) \\ Colin Barker, Oct 21 2014
(MAGMA) I:=[93645643, 12024611022569890927]; [n le 2 select I[n] else 128405450990*Self(n-1) - Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 10 2020
(Sage)
def A147527_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 93645643*x*(1-x)/(1 - 128405450990*x + x^2) ).list()
a=A147527_list(20); a[1:] # G. C. Greubel, Jan 10 2020
(GAP) a:=[93645643, 12024611022569890927];; for n in [3..20] do a[n]:=128405450990*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Jan 10 2020
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CROSSREFS
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Cf. A147528, A147529, A147530.
Sequence in context: A205665 A205465 A117624 * A293244 A136634 A033625
Adjacent sequences: A147524 A147525 A147526 * A147528 A147529 A147530
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KEYWORD
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easy,nonn
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AUTHOR
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Richard Choulet, Nov 06 2008
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EXTENSIONS
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Editing and a(6) from Colin Barker, Oct 21 2014
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STATUS
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approved
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