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%I #6 Nov 26 2023 08:37:46
%S 1,1,1,2,3,4,7,11,16,26,41,62,99,156,240,379,596,925,1453,2281,3556,
%T 5575,8742,13658,21394,33524,52432,82100,128597,201233,315058,493377,
%U 772247,1209008,1893055,2963414,4639389,7263831,11371536,17802783,27872601,43635714
%N G.f. A(x) satisfies A(x) = 1 / (1 - x - x^3 * A(x^3)).
%F a(0) = 1; a(n) = a(n-1) + Sum_{k=0..floor((n-3)/3)} a(k) * a(n-3-3*k).
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, (i-3)\3, v[j+1]*v[i-2-3*j])); v;
%Y Cf. A367659, A367666.
%Y Cf. A218032.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Nov 26 2023
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