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 A257487 #12 Dec 29 2024 16:34:23
%S A257487 4,5,13,44,160,593,2209,8240,30748,114749,428245,1598228,5964664,
%T A257487 22260425,83077033,310047704,1157113780,4318407413,16116515869,
%U A257487 60147656060,224474108368,837748777409,3126521001265,11668335227648,43546819909324
%N A257487 Expansion of ( -4+15*x-8*x^2 ) / ( (x-1)*(x^2-4*x+1) ).
%H A257487 M. Knor, R. Skrekovski, <a href="http://ajc.maths.uq.edu.au/pdf/58/ajc_v58_p119.pdf">Wiener index of generalized 4-stars and their quadratic line graphs</a>, Austral. J. Combinat. 58 (1) (2014) 119-126, eq. (11).
%H A257487 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,1).
%F A257487 a(n) = (5*A001353(n+1)-13*A001353(n)+3)/2. - _R. J. Mathar_, May 26 2016
%p A257487 A257487 := proc(n)
%p A257487 (5+sqrt(3))/4*(2-sqrt(3))^n+(5-sqrt(3))/4*(2+sqrt(3))^n+3/2 ;
%p A257487 expand(%) ;
%p A257487 end proc:
%p A257487 seq(A257487(n),n=0..30) ;
%t A257487 CoefficientList[Series[(-4+15x-8x^2)/((x-1)(x^2-4x+1)),{x,0,30}],x] (* or *) LinearRecurrence[{5,-5,1},{4,5,13},30] (* _Harvey P. Dale_, Dec 29 2024 *)
%o A257487 (PARI) Vec(( -4+15*x-8*x^2 ) / ( (x-1)*(x^2-4*x+1) ) + O(x^50)) \\ _Michel Marcus_, Apr 26 2015
%Y A257487 Cf. A055845 (first differences).
%K A257487 nonn,easy
%O A257487 0,1
%A A257487 _R. J. Mathar_, Apr 26 2015