A158643 a(n) = 676*n^2 + 26.

26, 702, 2730, 6110, 10842, 16926, 24362, 33150, 43290, 54782, 67626, 81822, 97370, 114270, 132522, 152126, 173082, 195390, 219050, 244062, 270426, 298142, 327210, 357630, 389402, 422526, 457002, 492830, 530010, 568542, 608426, 649662, 692250, 736190, 781482, 828126

Offset

0,1

Comments

The identity (52*n^2 + 1)^2 - (676*n^2 + 26)*(2*n)^2 = 1 can be written as A158644(n)^2 - a(n)*A005843(n)^2 = 1.

Links

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

Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]

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

Formula

G.f.: -26*(1 + 24*x + 27*x^2)/(x-1)^3.

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

From Amiram Eldar, Mar 19 2023: (Start)

Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(26))*Pi/sqrt(26) + 1)/52.

Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(26))*Pi/sqrt(26) + 1)/52. (End)

Mathematica

26(26Range[0, 40]^2+1) (* Harvey P. Dale, Mar 30 2011 *)
LinearRecurrence[{3, -3, 1}, {26, 702, 2730}, 50] (* Vincenzo Librandi, Feb 17 2012 *)

Prog

(Magma) I:=[26, 702, 2730]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 17 2012
(PARI) for(n=0, 40, print1(676*n^2 + 26", ")); \\ Vincenzo Librandi, Feb 17 2012

Crossrefs

Cf. A005843, A158644.

Sequence in context: A041313 A042302 A097835 * A181227 A094738 A182612

Adjacent sequences: A158640 A158641 A158642 * A158644 A158645 A158646

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 23 2009

Extensions

Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009

Status

approved