A027694 a(n) = n^2 + n + 9.
9, 11, 15, 21, 29, 39, 51, 65, 81, 99, 119, 141, 165, 191, 219, 249, 281, 315, 351, 389, 429, 471, 515, 561, 609, 659, 711, 765, 821, 879, 939, 1001, 1065, 1131, 1199, 1269, 1341, 1415, 1491, 1569, 1649, 1731, 1815, 1901, 1989, 2079, 2171, 2265, 2361, 2459, 2559
Offset: 0
Links
- 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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Maple
with (combinat):seq(fibonacci(3, n)+n+8, n=0..46); # Zerinvary Lajos, Jun 07 2008
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Mathematica
Table[n^2+n+9,{n,0,50}] (* Harvey P. Dale, Feb 07 2011 *) -
PARI
a(n)=n^2+n+9 \\ Charles R Greathouse IV, Oct 07 2015
Formula
For n > 3, a(n) = A176271(n+1,5). - Reinhard Zumkeller, Apr 13 2010
G.f.: (-9 + 16*x - 9*x^2)/(x-1)^3. - R. J. Mathar, Feb 07 2011
a(0) = 9, a(n) = a(n-1) + 2*n. - Vincenzo Librandi, Feb 07 2011
Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(35)/2)/sqrt(35). - Amiram Eldar, Jan 17 2021
From Elmo R. Oliveira, Oct 28 2024: (Start)
E.g.f.: exp(x)*(9 + 2*x + x^2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)