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
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).
Programs
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GAP
List([0..50],n->n^2+n+8); # Muniru A Asiru, Jul 15 2018
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Maple
with(combinat): seq(fibonacci(3, n)+n+7, n=0..46); # Zerinvary Lajos, Jun 07 2008
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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 *)
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PARI
a(n)=n^2+(n+8) \\ Charles R Greathouse IV, Jun 17 2017
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)