A187710 a(n) = n^2 + n + 10.
10, 12, 16, 22, 30, 40, 52, 66, 82, 100, 120, 142, 166, 192, 220, 250, 282, 316, 352, 390, 430, 472, 516, 562, 610, 660, 712, 766, 822, 880, 940, 1002, 1066, 1132, 1200, 1270, 1342, 1416, 1492, 1570, 1650, 1732, 1816, 1902, 1990, 2080, 2172, 2266, 2362, 2460
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[n^2 + n + 10: n in [0..50]]; // G. C. Greubel, Nov 06 2018
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Mathematica
f[n_] := n^2 + n + 10; f[Range[0, 100]] LinearRecurrence[{3, -3, 1}, {10, 12, 16}, 50] (* Harvey P. Dale, Jan 18 2014 *) -
PARI
a(n)=n^2+n+10 \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(0)=10, a(1)=12, a(2)=16; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jan 18 2014
From Bruno Berselli, Oct 20 2016: (Start)
G.f.: 2*(5 - 9*x + 5*x^2)/(1 - x)^3.
a(n) = 2*A167499(n-1) for n>0.
a(n) = Sum_{i=n-5..n+5} i*(i+1)/11. (End)
E.g.f.: (x^2 + 2*x + 10)*exp(x). - G. C. Greubel, Nov 06 2018
Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(39)/2)/sqrt(39). - Amiram Eldar, Jan 17 2021
Extensions
Offset changed to 0 from Bruno Berselli, Oct 20 2016