A144928 Values of k arising in A144927.

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

Offset

1,1

Comments

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

Links

Colin Barker, Table of n, a(n) for n = 1..450

Index entries for linear recurrences with constant coefficients, signature (110,-1).

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A144927.

Sequence in context: A109344 A129207 A243944 * A053772 A075416 A127861

Adjacent sequences: A144925 A144926 A144927 * A144929 A144930 A144931

Keyword

nonn,easy

Author

Richard Choulet, Sep 25 2008

Extensions

More terms from Colin Barker, Oct 17 2014

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

Status

approved