A144928 Values of k arising in A144927.

49, 5341, 587461, 64615369, 7107103129, 781716728821, 85981733067181, 9457208920661089, 1040206999539652609, 114413312740441125901, 12584424194448984196501, 1384172248076647820489209, 152246362864236811269616489, 16745715742817972591837324581

Offset: 1

Author

Richard Choulet, Sep 25 2008

Keywords

• nonn
• easy

Comments

Numbers k such that there exists x in N : (x+7)^3-x^3=k^2. - Richard Choulet, Oct 16 2008

Examples

			a(1) = 49 because (7+7)^3 - 7^3 = 2041 = 49^2. - _Richard Choulet_, Oct 16 2008
a(2) = 5341 because (1162+7)^3 - 1162^3 = 28526281 = 5341^2. - _Colin Barker_, Jul 16 2016
		

Links

• Colin Barker, Table of n, a(n) for n = 1..450
• Index entries for linear recurrences with constant coefficients, signature (110,-1).

Crossrefs

Cf. A144927.

Programs

Mathematica

Sqrt[(# + 7)^3 - #^3] & /@ Rest@ CoefficientList[Series[7 x (-1 - 55 x + 2 x^2)/((x - 1) (x^2 - 110 x + 1)), {x, 0, 14}], x] (* or *)
Rest@ CoefficientList[Series[49 x (1 - x)/(1 - 110 x + x^2), {x, 0, 14}], x] (* Michael De Vlieger, Jul 17 2016 *)

PARI

Vec(49*x*(1-x)/(1-110*x+x^2) + O(x^20)) \\ Colin Barker, Oct 17 2014, corrected Jul 16 2016

Formula

a(n+2) = 110*a(n+1)-a(n). - Richard Choulet, Oct 16 2008

G.f.: 49*x*(1-x) / (1-110*x+x^2). - Colin Barker, Oct 17 2014, corrected Jul 16 2016

Extensions

More terms from Colin Barker, Oct 17 2014

All terms except the first corrected by Colin Barker, Jul 16 2016