A184882 a(n) = 1 - 4*n - 4*n^2.

1, -7, -23, -47, -79, -119, -167, -223, -287, -359, -439, -527, -623, -727, -839, -959, -1087, -1223, -1367, -1519, -1679, -1847, -2023, -2207, -2399, -2599, -2807, -3023, -3247, -3479, -3719, -3967, -4223, -4487, -4759, -5039, -5327, -5623, -5927, -6239, -6559

Offset

0,2

Comments

Hankel transform of A184881.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1-10*x+x^2)/(1-x)^3.

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

a(0)=1, a(n) = a(n-1) - 8*n. - Vincenzo Librandi, Jan 25 2011

Sum_{n>=0} 1/a(n) = -tan(Pi/sqrt(2))*Pi/(4*sqrt(2)). - Amiram Eldar, Feb 03 2026

Mathematica

Table[1-4n-4n^2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, -7, -23}, 50] (* Harvey P. Dale, Feb 21 2014 *)

Prog

(Magma) [1-4*n-4*n^2: n in [0..60]]; // Vincenzo Librandi, Feb 23 2014
(PARI) a(n)=1-4*n-4*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A184881.

Sequence in context: A139035 A002146 A336092 * A073577 A379811 A348230

Adjacent sequences: A184879 A184880 A184881 * A184883 A184884 A184885

Keyword

sign,easy

Author

Paul Barry, Jan 24 2011

Status

approved