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

8827, 1133434915879903, 145539221541371657392445143, 18688029378753350610679552570834161667, 2399644840493193509137754319007833077692312755187, 308127477959355126566155341338642382333110448233345362623463

Offset: 1

Author

Richard Choulet, Nov 06 2008

Keywords

• easy
• nonn

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..50
• Index entries for linear recurrences with constant coefficients, signature (128405450990,-1).

Crossrefs

Cf. A147527, A147528, A147530.

Programs

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

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

Maple

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

Mathematica

LinearRecurrence[{128405450990,-1}, {8827,1133434915879903}, 20] (* G. C. Greubel, Jan 12 2020 *)

PARI

Vec(8827*x*(1-x)/(1-128405450990*x+x^2) + O(x^20)) \\ Colin Barker, Oct 21 2014

Sage

def A147529_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 8827*x*(1-x)/(1-128405450990*x+x^2) ).list()
a=A147529_list(20); a[1:] # G. C. Greubel, Jan 12 2020

Formula

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

G.f.: 8827*x*(1-x) / (1 - 128405450990*x + x^2). - Colin Barker, Oct 21 2014

Extensions

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