A241976 Values of k such that k^2 + (k+3)^2 is a square.

0, 9, 60, 357, 2088, 12177, 70980, 413709, 2411280, 14053977, 81912588, 477421557, 2782616760, 16218279009, 94527057300, 550944064797, 3211137331488, 18715879924137, 109084142213340, 635788973355909, 3705649697922120, 21598109214176817, 125883005587138788

Offset

1,2

Comments

A075841 gives the corresponding values of sqrt(n^2 + (n+3)^2).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Formula

G.f.: 3*x^2*(x-3) / ((x-1)*(x^2-6*x+1)).

a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3).

a(n) = 3*A001652(n-1).

a(n) = -3*(2 + (3-2*sqrt(2))^n*(1+sqrt(2)) - (-1+sqrt(2))*(3+2*sqrt(2))^n) / 4. - Colin Barker, Apr 13 2017

Example

9 is in the sequence because 9^2 + 12^2 = 225 = 15^2.

Mathematica

CoefficientList[Series[3 x (x - 3)/((x - 1) (x^2 - 6 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 11 2014 *)

Prog

(PARI) concat(0, Vec(3*x^2*(x-3)/((x-1)*(x^2-6*x+1)) + O(x^100)))

Crossrefs

Cf. A001652, A065113, A075841.

Sequence in context: A268965 A081904 A085373 * A082150 A026785 A153820

Adjacent sequences: A241973 A241974 A241975 * A241977 A241978 A241979

Keyword

nonn,easy

Author

Colin Barker, Aug 10 2014

Status

approved