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 A171069 #18 Nov 04 2024 13:25:35
%S A171069 0,1,1,12,25,169,480,2521,8425,38988,142129,615889,2352000,9845809,
%T A171069 38543569,158429388,628446025,2558296441,10219534560,41389108489,
%U A171069 165953373625,670283913612,2692893971041,10860865199521,43679923392000
%N A171069 G.f. -x*(x-1)*(1+x)/(1-x-12*x^2-x^3+x^4).
%C A171069 The member k=12 of a family of sequences starting 0,1,1,k with recurrence a(n) = a(n-1)+k*a(n-2)+a(n-3)-a(n-4).
%H A171069 Vincenzo Librandi, <a href="/A171069/b171069.txt">Table of n, a(n) for n = 0..1000</a>
%H A171069 Hugh Williams, R. K. Guy, <a href="http://dx.doi.org/10.1142/S1793042111004587">Some fourth-order linear divisibility sequences</a>, Intl. J. Number Theory vol. 7 (5) (2011) 1255-1277
%H A171069 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,12,1,-1).
%F A171069 a(n)= +a(n-1) +12*a(n-2) +a(n-3) -a(n-4).
%t A171069 CoefficientList[Series[-x*(x - 1)*(1 + x)/(1 - x - 12*x^2 - x^3 + x^4), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 19 2012 *)
%t A171069 LinearRecurrence[{1,12,1,-1},{0,1,1,12},30] (* _Harvey P. Dale_, Nov 04 2024 *)
%o A171069 (Magma) I:=[0, 1, 1, 12]; [n le 4 select I[n] else Self(n-1) + 12*Self(n-2) + Self(n-3) - Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 19 2012
%Y A171069 Cf. A116201 (k=1), A105309 (k=2), A152090 (k=3), A007598 (k=4), A005178 (k=5), A003757 (k=6).
%K A171069 nonn,easy
%O A171069 0,4
%A A171069 _R. J. Mathar_, at the request of _R. K. Guy_, Sep 03 2010