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G.f. A(x) satisfies A(x) = 1 / (1 - x * A(x^6)).
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%I #42 Dec 02 2023 08:12:41

%S 1,1,1,1,1,1,1,2,3,4,5,6,7,9,12,16,21,27,34,43,55,71,92,119,153,196,

%T 251,322,414,533,686,882,1133,1455,1869,2402,3088,3970,5103,6558,8427,

%U 10829,13917,17888,22992,29551,37979,48809,62727,80617,103612,133167

%N G.f. A(x) satisfies A(x) = 1 / (1 - x * A(x^6)).

%C This sequence is different from A005708.

%H Seiichi Manyama, <a href="/A367637/b367637.txt">Table of n, a(n) for n = 0..5000</a>

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/6)} a(k) * a(n-1-6*k).

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\6, v[j+1]*v[i-6*j])); v;

%Y Cf. A000621, A367794, A367800.

%Y Cf. A005708, A101916.

%K nonn

%O 0,8

%A _Seiichi Manyama_, Dec 01 2023