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 A062112 #21 Jun 04 2025 16:35:52
%S A062112 0,1,1,2,4,6,14,20,48,68,164,232,560,792,1912,2704,6528,9232,22288,
%T A062112 31520,76096,107616,259808,367424,887040,1254464,3028544,4283008,
%U A062112 10340096,14623104,35303296,49926400,120532992,170459392,411525376
%N A062112 a(0)=0; a(1)=1; a(n) = a(n-1) + (3 + (-1)^n)*a(n-2)/2.
%H A062112 Harry J. Smith, <a href="/A062112/b062112.txt">Table of n, a(n) for n = 0..200</a>
%H A062112 Sean A. Irvine, <a href="https://oeis.org/wiki/User:Sean_A._Irvine/Walks_on_Graphs#5_vertices">Walks on Graphs</a>.
%H A062112 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 4, 0, -2).
%F A062112 a(2*n) = A007070(n+1).
%F A062112 a(2*n+1) = A006012(n).
%F A062112 G.f.: x*(1+x-2*x^2)/(1-4*x^2+2*x^4).
%F A062112 a(n) = 4*a(n-2) - 2*a(n-4), a(0)=0, a(1)=1, a(2)=1, a(3)=2. - _Harvey P. Dale_, May 24 2013
%e A062112 a(4) = a(3) + 2*a(2) = 2 + 2 = 4.
%t A062112 RecurrenceTable[{a[0]==0,a[1]==1,a[n]==a[n-1]+(3+(-1)^n) (a[n-2])/2},a,{n,40}] (* or *) LinearRecurrence[{0,4,0,-2},{0,1,1,2},40] (* _Harvey P. Dale_, May 24 2013 *)
%o A062112 (PARI) { for (n=0, 200, if (n>1, a=a1 + (3 + (-1)^n)*a2/2; a2=a1; a1=a, if (n==0, a=a2=0, a=a1=1)); write("b062112.txt", n, " ", a) ) } \\ _Harry J. Smith_, Aug 01 2009
%o A062112 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x-2*x^2)/(1-4*x^2+2*x^4))); // _G. C. Greubel_, Oct 16 2018
%Y A062112 Cf. A006012, A007068, A007070.
%K A062112 easy,nonn
%O A062112 0,4
%A A062112 _Olivier Gérard_, Jun 05 2001