A082113 - OEIS

%I #13 Dec 23 2022 07:52:03

%S 1,7,37,127,337,751,1477,2647,4417,6967,10501,15247,21457,29407,39397,

%T 51751,66817,84967,106597,132127,162001,196687,236677,282487,334657,

%U 393751,460357,535087,618577,711487,814501,928327,1053697,1191367

%N a(n) = n^4 + 5*n^2 + 1.

%C Main diagonal of number array A082110.

%H G. C. Greubel, <a href="/A082113/b082113.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = n^4 + 5*n^2 + 1.

%F G.f.: (1+2*x+12*x^2+2*x^3+7*x^4) / (1-x)^5. - _R. J. Mathar_, Dec 03 2014

%F E.g.f.: (1 + 6*x + 12*x^2 + 6*x^3 + x^4)*exp(x). - _G. C. Greubel_, Dec 22 2022

%t Table[n^4+5n^2+1,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,7,37,127,337},40] (* _Harvey P. Dale_, May 16 2019 *)

%o (Magma) [n^4+5*n^2+1: n in [0..40]]; // _G. C. Greubel_, Dec 22 2022

%o (SageMath) [n^4+5*n^2+1 for n in range(41)] # _G. C. Greubel_, Dec 22 2022

%Y Cf. A082044, A082047, A082106.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 04 2003