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, 23370, 24528, 25714

Offset: 0

Author

Omar E. Pol, Oct 13 2011

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A135703, A144555, A152760, A193053, A195019, A195020, A195024, A195320, A198017.

Programs

Magma

[14*n^2 - 4*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011

Mathematica

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

PARI

a(n)=14*n^2-4*n \\ Charles R Greathouse IV, Apr 10 2012

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)

E.g.f.: 2*exp(x)*x*(5 + 7*x). - Elmo R. Oliveira, Dec 30 2024

Extensions

Corrected by Vincenzo Librandi, Oct 14 2011