A144965 a(n) = 4*n*(4*n^2+1).

0, 20, 136, 444, 1040, 2020, 3480, 5516, 8224, 11700, 16040, 21340, 27696, 35204, 43960, 54060, 65600, 78676, 93384, 109820, 128080, 148260, 170456, 194764, 221280, 250100, 281320, 315036, 351344, 390340, 432120, 476780, 524416, 575124

Offset

0,2

Comments

(a(n))^2 + (n*a(n)+1)^2 is always a perfect square.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Luc Comeau-Montasse, Des mesures entières pour des triangles rectangles, Géométrie et nombre (French blog), September 2008.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: 4*x*(5+14*x+5*x^2)/(1-x)^4. [Colin Barker, May 24 2012]

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jun 30 2012

Mathematica

CoefficientList[Series[4*x*(5+14*x+5*x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 30 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 20, 136, 444}, 50] (* Harvey P. Dale, Aug 07 2022 *)

Prog

(Magma) I:=[0, 20, 136, 444]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 30 2012

Crossrefs

Cf. A053755 (4*n^2+1).

Sequence in context: A168178 A085284 A105573 * A262140 A140301 A264315

Adjacent sequences: A144962 A144963 A144964 * A144966 A144967 A144968

Keyword

easy,nonn

Author

Luc Comeau-Montasse, Sep 27 2008

Status

approved