login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n) = n^2 + n + 10.
3

%I #23 Sep 08 2022 08:45:56

%S 10,12,16,22,30,40,52,66,82,100,120,142,166,192,220,250,282,316,352,

%T 390,430,472,516,562,610,660,712,766,822,880,940,1002,1066,1132,1200,

%U 1270,1342,1416,1492,1570,1650,1732,1816,1902,1990,2080,2172,2266,2362,2460

%N a(n) = n^2 + n + 10.

%H G. C. Greubel, <a href="/A187710/b187710.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F 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

%F From _Bruno Berselli_, Oct 20 2016: (Start)

%F G.f.: 2*(5 - 9*x + 5*x^2)/(1 - x)^3.

%F a(n) = 2*A167499(n-1) for n>0.

%F a(n) = Sum_{i=n-5..n+5} i*(i+1)/11. (End)

%F E.g.f.: (x^2 + 2*x + 10)*exp(x). - _G. C. Greubel_, Nov 06 2018

%F Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(39)/2)/sqrt(39). - _Amiram Eldar_, Jan 17 2021

%t f[n_] := n^2 + n + 10; f[Range[0, 100]]

%t LinearRecurrence[{3, -3, 1}, {10, 12, 16}, 50] (* _Harvey P. Dale_, Jan 18 2014 *)

%o (PARI) a(n)=n^2+n+10 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Magma) [n^2 + n + 10: n in [0..50]]; // _G. C. Greubel_, Nov 06 2018

%Y Cf. A002061, A002378, A167499.

%K nonn,easy

%O 0,1

%A _Vladimir Joseph Stephan Orlovsky_, Mar 12 2011

%E Offset changed to 0 from _Bruno Berselli_, Oct 20 2016