This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A166957 #34 May 10 2025 03:16:12
%S A166957 1,1131,7829,25141,58113,111791,191221,301449,447521,634483,867381,
%T A166957 1151261,1491169,1892151,2359253,2897521,3512001,4207739,4989781,
%U A166957 5863173,6832961,7904191,9081909,10371161,11776993,13304451
%N A166957 a(n) = 841*n^3 + 261*n^2 + 28*n + 1.
%C A166957 Polynomials in one variable have a certain property viz f(x+f(x)) == 0 (mod f(x)). This is true even when the polynomial is in two variables (not necessarily homogeneous). This sequence is a demonstration when the polynomial is x^3 + 2*x*y + y^2 (x = 2, y=3).
%C A166957 When x = 2 and y=3, f(x,y) = 29. Hence f((2 + 29), (3 + 29))/29 = 1131.
%H A166957 Vincenzo Librandi, <a href="/A166957/b166957.txt">Table of n, a(n) for n = 0..1000</a>
%H A166957 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A166957 a(n) = 841*n^3 + 261*n^2 + 28*n + 1.
%F A166957 G.f.: x*(1131 + 3305*x + 611*x^2 - x^3)/(1-x)^4 . - _R. J. Mathar_, Sep 02 2011
%F A166957 a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - _Vincenzo Librandi_, Jul 01 2012
%F A166957 E.g.f.: (1 + 1130*x + 2784*x^2 + 841*x^3)*exp(x). - _G. C. Greubel_, Apr 09 2016
%p A166957 seq(1 +28*n +261*n^2 +841*n^3, n=0..40); # _G. C. Greubel_, Sep 02 2019
%t A166957 CoefficientList[Series[(1131+3305*x+611*x^2-x^3)/(x-1)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jul 01 2012 *)
%t A166957 Table[841n^3+261n^2+28n+1,{n,30}] (* or *) LinearRecurrence[{4,-6,4,-1},{1131,7829,25141,58113},30] (* _Harvey P. Dale_, Apr 11 2013 *)
%o A166957 (PARI) a(n) = ((2+n*29)^3 + 2*(2+n*29)*(3+n*29) + (3+n*29)^2)/29
%o A166957 (Magma) I:=[1131, 7829, 25141, 58113]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jul 01 2012
%o A166957 (Magma) [1 +28*n +261*n^2 +841*n^3: n in [0..40]]; // _G. C. Greubel_, Sep 02 2019
%o A166957 (Sage) [1 +28*n +261*n^2 +841*n^3 for n in (0..40)] # _G. C. Greubel_, Sep 02 2019
%o A166957 (GAP) List([0..40], n-> 1 +28*n +261*n^2 +841*n^3); # _G. C. Greubel_, Sep 02 2019
%Y A166957 Cf. A165806, A165808, A165809.
%K A166957 nonn,easy
%O A166957 0,2
%A A166957 _A.K. Devaraj_, Oct 25 2009
%E A166957 Formula, description, editing, and program correction by _Charles R Greathouse IV_, Nov 04 2009
%E A166957 a(0)=1 added by _N. J. A. Sloane_, Apr 09 2016