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 A189836 a(n) = n^2 + 11. 5

%I

%S 11,12,15,20,27,36,47,60,75,92,111,132,155,180,207,236,267,300,335,

%T 372,411,452,495,540,587,636,687,740,795,852,911,972,1035,1100,1167,

%U 1236,1307,1380,1455,1532,1611,1692,1775,1860,1947

%N a(n) = n^2 + 11.

%H G. C. Greubel, <a href="/A189836/b189836.txt">Table of n, a(n) for n = 0..10000</a>

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

%F From _G. C. Greubel_, Jan 13 2018: (Start)

%F G.f.: (11 - 21*x + 12*x^2)/(1 - x)^3.

%F E.g.f.: (11 + x + x^2)*exp(x). (End)

%F From _Amiram Eldar_, Nov 02 2020: (Start)

%F Sum_{n>=0} 1/a(n) = (1 + sqrt(11)*Pi*coth(sqrt(11)*Pi))/22.

%F Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(11)*Pi*cosech(sqrt(11)*Pi))/22. (End)

%t Table[n^2+11,{n,0,100}]

%t LinearRecurrence[{3,-3,1},{11,12,15},60] (* _Harvey P. Dale_, Aug 24 2020 *)

%o (PARI) a(n)=n^2+11 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (MAGMA) [n^2 + 11: n in [0..50]]; // _G. C. Greubel_, Jan 13 2018

%Y Cf. A002522, A059100, A117950, A087475.

%K nonn,easy

%O 0,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 28 2011

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Last modified November 26 03:20 EST 2020. Contains 338632 sequences. (Running on oeis4.)