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 A180510 #50 Jan 05 2023 19:08:54
%S A180510 0,1,1,2,7,5,20,27,49,106,155,331,560,1013,1917,3310,6223,11117,20140,
%T A180510 36899,66185,121014,218791,396703,721280,1305025,2371433,4298618,
%U A180510 7796439,14150029,25652500,46550531,84427441,153141122,277824947,503893035,914114320,1658100757,3007674389,5455918726,9896444495,17951959061,32563657260
%N A180510 G.f.: (t^5 + 2*t^4 + t^3 + 2*t^2 + t) / (t^6 + t^5 - 2*t^4 - 5*t^3 - 2*t^2 + t + 1).
%C A180510 An example of a sextic divisibility sequence whose characteristic polynomial has degree 6 and a 12-element dihedral Galois group. This example has a field and polynomial discriminant of 98000, which is one of the smallest possible.
%D A180510 Found by Noam D. Elkies and described in an email from Elkies to R. K. Guy, Jan 18 2011
%H A180510 Vincenzo Librandi, <a href="/A180510/b180510.txt">Table of n, a(n) for n = 0..300</a> (corrected by Ray Chandler, Jan 19 2019)
%H A180510 E. L. Roettger, H. C. Williams, and R. K. Guy, <a href="https://carma.newcastle.edu.au/meetings/alfcon/pdfs/Hugh_Williams-alfcon.pdf">Some extensions of the Lucas functions</a>, Number Theory and Related Fields: In Memory of Alf van der Poorten, Series: Springer Proceedings in Mathematics & Statistics, Vol. 43, J. Borwein, I. Shparlinski, W. Zudilin (Eds.) 2013.
%H A180510 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A180510 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2,5,2,-1,-1).
%F A180510 a(n) = -a(-n) for all n in Z. - _Michael Somos_, Dec 30 2022
%e A180510 G.f. = x + x^2 + 2*x^3 + 7*x^4 + 5*x^5 + 20*x^6 + 27*x^7 + 49*x^8 + 106*x^9 + ... - _Michael Somos_, Dec 30 2022
%t A180510 CoefficientList[ Series[(x^5 + 2x^4 + x^3 + 2x^2 + x)/(x^6 + x^5 - 2x^4 - 5x^3 - 2x^2 + x + 1), {x, 0, 42}], x] (* _Robert G. Wilson v_, Jun 26 2011 *)
%t A180510 a[1] = 0; a[2] = 1; a[3] = 1; a[4] = 2; a[5] = 7; a[6] = 5; a[n_Integer] := a[n] = -a[n - 6] - a[n - 5] + 2 a[n - 4] + 5 a[n - 3] + 2 a[n - 2] - a[n - 1] (* Or *)
%t A180510 LinearRecurrence[{-1, 2, 5, 2, -1, -1}, {0, 1, 1, 2, 7, 5}, 43] (* _Roger L. Bagula_, Mar 16 2012 *)
%t A180510 a[ n_] := a[n] = Sign[n]*With[{m = Abs[n]}, If[ m<4, {0, 1, 1, 2}[[m+1]], -a[m-1] +2*a[m-2] +5*a[m-3] +2*a[m-4] -a[m-5] -a[m-6]]]; (* _Michael Somos_, Dec 30 2022 *)
%o A180510 (Maxima) makelist(coeff(taylor(x*(x^4+2*x^3+x^2+2*x+1)/(x^6+x^5-2*x^4-5*x^3-2*x^2+x+1), x, 0, n), x, n), n, 1, 42); /* _Bruno Berselli_, Jun 05 2011 */
%o A180510 (PARI) Vec((x^5+2*x^4+x^3+2*x^2+x)/(x^6+x^5-2*x^4-5*x^3-2*x^2+x+1)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 06 2011
%o A180510 (PARI) {a(n) = sign(n)*polcoeff((x^5 + 2*x^4 + x^3 + 2*x^2 + x)/(x^6 + x^5 - 2*x^4 - 5*x^3 - 2*x^2 + x + 1) + x*O(x^abs(n)), abs(n))}; /* _Michael Somos_, Dec 30 2022 */
%Y A180510 Cf. A001351, A001945, A005120, A006235.
%K A180510 nonn,easy
%O A180510 0,4
%A A180510 _N. J. A. Sloane_, Jan 20 2011