A367660 - OEIS

%I #8 Nov 26 2023 08:37:28

%S 1,2,4,8,16,34,72,152,320,676,1428,3016,6368,13448,28400,59976,126656,

%T 267472,564848,1192848,2519056,5319746,11234248,23724504,50101440,

%U 105804296,223437672,471856016,996466240,2104338904,4443946064,9384731992,19818691136

%N G.f. A(x) satisfies A(x) = 1 / (1 - x - x * A(x^4)).

%F a(0) = 1; a(n) = a(n-1) + Sum_{k=0..floor((n-1)/4)} a(k) * a(n-1-4*k).

%F a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 8; a(n) = a(n-4) + Sum_{k=0..n-1} a(floor(k/4)) * a(n-1-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-1)\4, v[j+1]*v[i-4*j])); v;

%Y Cf. A349365, A367659, A367661.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 26 2023