login
A144928
Values of k arising in A144927.
4
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
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
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