A158553 a(n) = 196*n^2 - 14.

182, 770, 1750, 3122, 4886, 7042, 9590, 12530, 15862, 19586, 23702, 28210, 33110, 38402, 44086, 50162, 56630, 63490, 70742, 78386, 86422, 94850, 103670, 112882, 122486, 132482, 142870, 153650, 164822, 176386, 188342, 200690, 213430, 226562, 240086, 254002, 268310

Offset

1,1

Comments

The identity (28*n^2 - 1)^2 - (196*n^2 - 14)*(2*n)^2 = 1 can be written as A158554(n)^2 - a(n)*A005843(n)^2 = 1.

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

G.f.: 14*x*(13 + 16*x - x^2)/(1-x)^3.

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

From Amiram Eldar, Mar 09 2023: (Start)

Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(14))*Pi/sqrt(14))/28.

Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(14))*Pi/sqrt(14) - 1)/28. (End)

Mathematica

LinearRecurrence[{3, -3, 1}, {182, 770, 1750}, 40] (* Vincenzo Librandi, Feb 14 2012 *)
196*Range[40]^2-14 (* Harvey P. Dale, Oct 11 2023 *)

Prog

(Magma) I:=[182, 770, 1750]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 14 2012
(PARI) for(n=1, 40, print1(196*n^2 - 14", ")); \\ Vincenzo Librandi, Feb 14 2012

Crossrefs

Cf. A005843, A158554.

Sequence in context: A145297 A056091 A272361 * A015883 A043463 A047636

Adjacent sequences: A158550 A158551 A158552 * A158554 A158555 A158556

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 21 2009

Extensions

Comment rewritten by R. J. Mathar, Oct 16 2009

Status

approved