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A242575 a(n) = [x^n] G(n+1,x) where G(n,x) is the n-th iteration of G(1,x) = x/(1-x+x^2), so that G(n+1,x) = G(n, G(1,x)) with G(0,x)=x.

%I A242575 #5 May 17 2014 19:09:11
%S A242575 1,3,12,65,464,4235,48000,658197,10676571,200994145,4321369524,
%T A242575 104676808756,2824120458186,84038944594677,2735391623889696,
%U A242575 96690702098948611,3688764754855986702,151064345601782722492,6609564176073032406148,307682727619722793499662
%N A242575 a(n) = [x^n] G(n+1,x) where G(n,x) is the n-th iteration of G(1,x) = x/(1-x+x^2), so that G(n+1,x) = G(n, G(1,x)) with G(0,x)=x.
%H A242575 Paul D. Hanna, <a href="/A242575/b242575.txt">Table of n, a(n) for n = 1..200</a>
%e A242575 Given x/(1-x+x^2) = x + x^2 - x^4 - x^5 + x^7 + x^8 - x^10 - x^11 + x^13 +...
%e A242575 form a table of coefficients in the iterations of x/(1-x+x^2) like so:
%e A242575 [1,  1,  0,  -1,   -1,     0,      1,       1,        0,       -1, ...];
%e A242575 [1,  2,  2,  -1,   -8,   -15,    -10,      22,       79,      112, ...];
%e A242575 [1,  3,  6,   6,  -11,   -73,   -201,    -309,       37,     1913, ...];
%e A242575 [1,  4, 12,  26,   24,  -116,   -808,   -3000,    -7566,    -9882, ...];
%e A242575 [1,  5, 20,  65,  155,   120,  -1379,  -10761,   -51202,  -183269, ...];
%e A242575 [1,  6, 30, 129,  464,  1225,    702,  -18978,  -169139,  -994138, ...];
%e A242575 [1,  7, 42, 224, 1057,  4235,  12411,    4445,  -301321, -3076795, ...];
%e A242575 [1,  8, 56, 356, 2064, 10752,  48000,  156416,    27812, -5458012, ...];
%e A242575 [1,  9, 72, 531, 3639, 23064, 132633,  658197,  2388060,   187911, ...];
%e A242575 [1, 10, 90, 755, 5960, 44265, 306742, 1942198, 10676571, 43159172, ...]; ...
%e A242575 then this sequence forms a diagonal in the above table.
%o A242575 (PARI) {a(n)=local(A=x, G=x/(1-x+x^2)); for(i=1, n+1, A=subst(G, x, A+x*O(x^(n)))); polcoeff(A, n)}
%o A242575 for(n=1,30,print1(a(n),", "))
%Y A242575 Cf. A242573, A242574.
%K A242575 nonn
%O A242575 1,2
%A A242575 _Paul D. Hanna_, May 17 2014