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

Offset

0,1

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).

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

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 *)

Prog

(PARI) a(n)=n^2+n+4 \\ Charles R Greathouse IV, Oct 07 2015
(GAP) List([0..50], n->n^2+n+4); # Muniru A Asiru, Jul 15 2018

Crossrefs

Cf. A000217, A002522.

Sequence in context: A107305 A102768 A075637 * A023501 A050887 A078642

Adjacent sequences: A027686 A027687 A027688 * A027690 A027691 A027692

Keyword

nonn,easy

Author

Patrick De Geest

Status

approved