A108928 a(n) = 8*n^2 - 3.

5, 29, 69, 125, 197, 285, 389, 509, 645, 797, 965, 1149, 1349, 1565, 1797, 2045, 2309, 2589, 2885, 3197, 3525, 3869, 4229, 4605, 4997, 5405, 5829, 6269, 6725, 7197, 7685, 8189, 8709, 9245, 9797, 10365, 10949, 11549, 12165, 12797, 13445, 14109, 14789

Offset: 1

Author

Marcel Hetkowski Fabeny (marcelfabeny(AT)yahoo.com.br), Jul 19 2005

Keywords

• easy
• nonn

Comments

Sequence found by reading the segment (5, 29) together with the line from 29, in the direction 29, 69,..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 04 2011

Examples

			(1*3 = 3)+2 = 5; (3*5 = 15)+14 = 29; (5*7 = 35)+34 = 69; (7*9 = 63)+62 = 125; ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

Magma

[8*n^2 - 3: n in [1..50]]; // Vincenzo Librandi, Sep 05 2011

Maple

seq(8*n^2-3,n=1..50); # Emeric Deutsch, Aug 01 2005

Mathematica

8*Range[50]^2-3 (* or *) LinearRecurrence[{3,-3,1},{5,29,69},50] (* Harvey P. Dale, Jul 21 2012 *)

PARI

a(n)=8*n^2-3 \\ Charles R Greathouse IV, Sep 04 2011

Formula

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

a(1)=5, a(2)=29, a(3)=69, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jul 21 2012

From G. C. Greubel, Jul 15 2017:(Start)

G.f.: x*(-5 - 14*x + 3*x^2)/(-1 + x)^3.

E.g.f.: (8*x^2 + 8*x - 3)*exp(x) + 3. (End)

Extensions

More terms from Emeric Deutsch, Aug 01 2005