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

51721, 6641322533431006, 852782015075257741682069713, 109501859241899449111168441436054160358, 14060635620199598267351285586436862449157290510201, 1805462258017787769335954916623470050495526664967434749114126

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..90

Index entries for linear recurrences with constant coefficients, signature (128405450991,-128405450991,1).

Formula

a(n+2) = 128405450990*a(n+1) - a(n) + 62402725494.

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

Example

a(1)=51721 because the first relation is : 51722^3 - 51721^3 = 103*8827^2.

Maple

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

Mathematica

LinearRecurrence[{128405450991, -128405450991, 1}, {51721, 6641322533431006, 852782015075257741682069713}, 20] (* G. C. Greubel, Jan 12 2020 *)

Prog

(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
(PARI) isok(x) = issquare(((x+1)^3-x^3)/103) \\ Colin Barker, Jul 13 2016
(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
(Sage)
def A147530_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x + x^2)) ).list()
a=A147530_list(20); a[1:] # G. C. Greubel, Jan 12 2020
(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

Crossrefs

Cf. A147527, A147528, A147529.

Sequence in context: A344645 A203354 A289823 * A184454 A003134 A253989

Adjacent sequences: A147527 A147528 A147529 * A147531 A147532 A147533

Keyword

nonn,easy

Author

Richard Choulet, Nov 06 2008

Extensions

Editing and a(6) from Colin Barker, Oct 21 2014

a(3) to a(6) corrected by Colin Barker, Jul 13 2016

Status

approved