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%I #12 Nov 30 2023 16:10:35
%S 1,2,3,4,5,8,13,20,29,43,66,102,155,233,352,536,817,1240,1878,2848,
%T 4327,6576,9984,15150,22995,34919,53029,80513,122224,185556,281736,
%U 427776,649481,986054,1497069,2272976,3451038,5239607,7955067,12077876,18337503
%N G.f. A(x) satisfies A(x) = 1 / ((1 - x) * (1 - x * A(x^4))).
%F a(n) = 1 + Sum_{k=0..floor((n-1)/4)} a(k) * a(n-1-4*k).
%o (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, (i-1)\4, v[j+1]*v[i-4*j])); v;
%o (Python)
%o from functools import lru_cache
%o @lru_cache(maxsize=None)
%o def A367692(n): return 1+sum(A367692(k)*A367692(n-1-(k<<2)) for k in range(n+3>>2)) # _Chai Wah Wu_, Nov 30 2023
%Y Cf. A007317, A351972, A367691.
%Y Cf. A367660.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Nov 27 2023
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