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a(n) = Sum_{k=0..floor(n/3)} binomial(n-3*k,floor(k/3)).
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%I #11 Oct 02 2024 07:53:20

%S 1,1,1,2,2,2,3,3,3,3,4,5,6,8,10,12,15,18,21,24,28,33,39,47,57,69,84,

%T 102,123,147,175,208,247,294,351,420,504,606,729,876,1051,1259,1506,

%U 1800,2151,2571,3075,3681,4410,5286,6337,7596,9102,10902,13053,15624,18699,22380,26790

%N a(n) = Sum_{k=0..floor(n/3)} binomial(n-3*k,floor(k/3)).

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1).

%F G.f.: (1-x^9)/((1-x^3) * (1-x*(1+x^9))) = (1+x^3+x^6)/(1-x*(1+x^9)).

%F a(n) = a(n-1) + a(n-10).

%o (PARI) a(n) = sum(k=0, n\3, binomial(n-3*k, k\3));

%o (PARI) my(N=60, x='x+O('x^N)); Vec((1+x^3+x^6)/(1-x*(1+x^9)))

%Y Cf. A003269, A098527.

%Y Cf. A376649.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Oct 01 2024