A065532 a(n) = 48*n^2 - 1.

-1, 47, 191, 431, 767, 1199, 1727, 2351, 3071, 3887, 4799, 5807, 6911, 8111, 9407, 10799, 12287, 13871, 15551, 17327, 19199, 21167, 23231, 25391, 27647, 29999, 32447, 34991, 37631, 40367, 43199, 46127, 49151, 52271, 55487, 58799, 62207, 65711, 69311, 73007, 76799

Offset: 0

Author

Labos Elemer, Nov 28 2001

Keywords

• sign
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A158463.

Programs

Magma

[48*n^2 - 1: n in [0..50]]; // Vincenzo Librandi, Jul 08 2012

Mathematica

CoefficientList[Series[(1-50*x-47*x^2)/(x-1)^3,{x,0,40}],x] (* Vincenzo Librandi, Jul 08 2012 *)
LinearRecurrence[{3,-3,1},{-1,47,191},40] (* Harvey P. Dale, Dec 13 2017 *)

PARI

A065532(n)=48*n^2-1

Formula

From Vincenzo Librandi, Jul 08 2012: (Start)

G.f.: (1 - 50*x - 47*x^2)/(x-1)^3.

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

From Amiram Eldar, Mar 19 2023: (Start)

Sum_{n>=1} 1/a(n) = (1 - cot(Pi/(4*sqrt(3)))*Pi/(4*sqrt(3)))/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/(4*sqrt(3)))*Pi/(4*sqrt(3)) - 1)/2. (End)

From Elmo R. Oliveira, Jan 16 2025: (Start)

E.g.f.: exp(x)*(48*x^2 + 48*x - 1).

a(n) = A158463(2*n). (End)

Extensions

Better description from Randall L Rathbun, Jan 19 2002

Offset changed from 1 to 0 by Harry J. Smith, Oct 21 2009