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

1,1

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

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)

Example

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

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 *)

Prog

(PARI) a(n)=8*n^2-3 \\ Charles R Greathouse IV, Sep 04 2011
(Magma) [8*n^2 - 3: n in [1..50]]; // Vincenzo Librandi, Sep 05 2011

Crossrefs

Sequence in context: A341085 A301858 A293174 * A097812 A176333 A100559

Adjacent sequences: A108925 A108926 A108927 * A108929 A108930 A108931

Keyword

easy,nonn

Author

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

Extensions

More terms from Emeric Deutsch, Aug 01 2005

Status

approved