A195023 a(n) = 14*n^2 - 4*n.

0, 10, 48, 114, 208, 330, 480, 658, 864, 1098, 1360, 1650, 1968, 2314, 2688, 3090, 3520, 3978, 4464, 4978, 5520, 6090, 6688, 7314, 7968, 8650, 9360, 10098, 10864, 11658, 12480, 13330, 14208, 15114, 16048, 17010, 18000, 19018, 20064, 21138, 22240

Offset

0,2

Comments

Sequence found by reading the line from 0, in the direction 0, 10, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the one of the semi-axis of the square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Formula

a(n) = 2*A135703(n). - Bruno Berselli, Oct 13 2011

From Colin Barker, Apr 09 2012: (Start)

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

G.f.: 2*x*(5+9*x)/(1-x)^3. (End)

Mathematica

Table[14n^2-4n, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 10, 48}, 50] (* Harvey P. Dale, Sep 05 2012 *)

Prog

(Magma) [14*n^2 - 4*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011
(PARI) a(n)=14*n^2-4*n \\ Charles R Greathouse IV, Apr 10 2012

Crossrefs

Cf. A144555, A152760, A195019, A195020, A195024, A195320, A185019, A193053, A198017.

Sequence in context: A121075 A121073 A210371 * A353620 A277229 A163724

Adjacent sequences: A195020 A195021 A195022 * A195024 A195025 A195026

Keyword

nonn,easy

Author

Omar E. Pol, Oct 13 2011

Extensions

Corrected by Vincenzo Librandi, Oct 14 2011

Status

approved