A027693 a(n) = n^2 + n + 8.

8, 10, 14, 20, 28, 38, 50, 64, 80, 98, 118, 140, 164, 190, 218, 248, 280, 314, 350, 388, 428, 470, 514, 560, 608, 658, 710, 764, 820, 878, 938, 1000, 1064, 1130, 1198, 1268, 1340, 1414, 1490, 1568, 1648, 1730, 1814, 1900, 1988, 2078, 2170, 2264, 2360, 2458, 2558

Offset

0,1

Links

Muniru A Asiru, Table of n, a(n) for n = 0..4000

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) = 2*n + a(n-1) (with a(0)=8). - Vincenzo Librandi, Aug 05 2010

From Harvey P. Dale, Dec 13 2011: (Start)

a(0)=8, a(1)=10, a(2)=14, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: (2*(7-4*x)*x-8)/(x-1)^3. (End)

Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(31)/2)/sqrt(31). - Amiram Eldar, Jan 17 2021

From Elmo R. Oliveira, Oct 31 2024: (Start)

E.g.f.: exp(x)*(8 + 2*x + x^2).

a(n) = 2*A145018(n+1). (End)

Maple

with(combinat): seq(fibonacci(3, n)+n+7, n=0..46); # Zerinvary Lajos, Jun 07 2008

Mathematica

f[n_]:=n^2+n+8; f[Range[0, 100]] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2011 *)
LinearRecurrence[{3, -3, 1}, {8, 10, 14}, 60] (* Harvey P. Dale, Dec 13 2011 *)

Prog

(PARI) a(n)=n^2+(n+8) \\ Charles R Greathouse IV, Jun 17 2017
(GAP) List([0..50], n->n^2+n+8); # Muniru A Asiru, Jul 15 2018

Crossrefs

Cf. A002061, A002378, A002522, A145018.

Sequence in context: A262708 A134321 A326386 * A196226 A250290 A228946

Adjacent sequences: A027690 A027691 A027692 * A027694 A027695 A027696

Keyword

nonn,easy

Author

Patrick De Geest

Status

approved