A027689 a(n) = n^2 + n + 4.

4, 6, 10, 16, 24, 34, 46, 60, 76, 94, 114, 136, 160, 186, 214, 244, 276, 310, 346, 384, 424, 466, 510, 556, 604, 654, 706, 760, 816, 874, 934, 996, 1060, 1126, 1194, 1264, 1336, 1410, 1486, 1564, 1644, 1726, 1810, 1896, 1984, 2074, 2166, 2260, 2356, 2454, 2554

Offset: 0

Author

Patrick De Geest

Keywords

• nonn
• easy

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..2000
• Patrick De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X).
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A002522, A152948.

Programs

GAP

List([0..50],n->n^2+n+4); # Muniru A Asiru, Jul 15 2018

Maple

with (combinat):seq(fibonacci(3, n)+n+3, n=0..47); # Zerinvary Lajos, Jun 07 2008

Mathematica

Table[n^2+n+4,{n,0,100}] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2011 *)
LinearRecurrence[{3,-3,1},{4,6,10},50] (* or *) CoefficientList[ Series[ (-4+6*x-4*x^2)/(-1+x)^3,{x,0,50}],x] (* Harvey P. Dale, Dec 18 2021 *)

PARI

a(n)=n^2+n+4 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = A000217(n-2) + A000217(n+2) for n > 0. - Jon Perry, Jul 23 2003

a(n) = 2*n + a(n-1)-2 (with a(1)=4). - Vincenzo Librandi, Aug 05 2010

Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(15)/2)/sqrt(15). - Amiram Eldar, Jan 18 2021

From Elmo R. Oliveira, Oct 28 2024: (Start)

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

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

a(n) = 2*A152948(n+2). (End)