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 A101917 #33 Mar 01 2022 12:00:10
%S A101917 1,-1,1,-1,1,-1,1,-1,2,-3,4,-5,6,-7,8,-10,13,-17,22,-28,35,-43,53,-66,
%T A101917 83,-105,133,-168,211,-264,330,-413,518,-651,819,-1030,1294,-1624,
%U A101917 2037,-2555,3206,-4025,5055,-6349,7973,-10010,12565,-15771,19796,-24851,31200,-39173,49183,-61748,77519,-97315,122166
%N A101917 G.f. satisfies: A(x) = 1/(1 + x*A(x^7)) and also the continued fraction: 1 + x*A(x^8) = [1; 1/x, 1/x^7, 1/x^49, 1/x^343, ..., 1/x^(7^(n-1)), ...].
%F A101917 This was conjectured to have g.f. (1+x^7) / (1+x+x^7) by _Ralf Stephan_, May 17 2007, but this is wrong. This g.f. produces a sequence which differs at a(57) = -153367. The g.f. gives a(57) = -153366. - _Johannes W. Meijer_, Aug 08 2011
%F A101917 a(0) = 1; a(n) = -Sum_{k=0..floor((n-1)/7)} a(k) * a(n-7*k-1). - _Ilya Gutkovskiy_, Mar 01 2022
%p A101917 nmax:=57: kmax:=nmax: for k from 0 to kmax do A:= proc(x): add(A101917(n)*x^n, n=0..k) end: f(x):=series(1/(1 + x*A(x^7)),x,k+1); for n from 0 to k do x(n):=coeff(f(x),x,n) od: A101917(k):=x(k): od: seq(A101917(n), n=0..nmax); # _Johannes W. Meijer_, Aug 08 2011
%t A101917 m = 57; A[_] = 0; Do[A[x_] = 1/(1 + x A[x^7]) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* _Jean-François Alcover_, Nov 03 2019 *)
%o A101917 (PARI) a(n)=local(A);A=1-x;for(i=1,n\7+1, A=1/(1+x*subst(A,x,x^7)+x*O(x^n)));polcoeff(A,n,x)
%o A101917 (PARI) a(n)=local(M=contfracpnqn(concat(1, vector(ceil(log(n+1)/log(7))+1,n,1/x^(7^(n-1)))))); polcoeff(M[1,1]/M[2,1]+x*O(x^(8*n+1)),8*n+1)
%Y A101917 Cf. A101912, A101913, A101914, A101915, A101916, A101918.
%K A101917 sign
%O A101917 0,9
%A A101917 _Paul D. Hanna_, Dec 20 2004