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A371458 Expansion of 1/(1 - x/(1 - 9*x^3)^(1/3)).

%I A371458 #34 Jun 11 2024 08:30:39
%S A371458 1,1,1,1,4,7,10,31,61,100,274,565,1000,2551,5380,10000,24376,52018,
%T A371458 100000,236389,507706,1000000,2313346,4986178,10000000,22773334,
%U A371458 49180165,100000000,225092416,486575935,1000000000,2231117230,4824998773,10000000000
%N A371458 Expansion of 1/(1 - x/(1 - 9*x^3)^(1/3)).
%F A371458 a(3*n) = 10^(n-1) for n > 0.
%F A371458 a(n) = Sum_{k=0..floor(n/3)} 9^k * binomial(n/3-1,k).
%F A371458 D-finite with recurrence (n-1)*(n-2)*a(n) +4*(-7*n^2+48*n-86)*a(n-3) +9*(29*n-141)*(n-6)*a(n-6) -810*(n-6)*(n-9)*a(n-9)=0. - _R. J. Mathar_, Jun 07 2024
%F A371458 a(n) == 1 (mod 3). - _Seiichi Manyama_, Jun 11 2024
%p A371458 A371458 := proc(n)
%p A371458     add(9^k*binomial(n/3-1,k),k=0..floor(n/3)) ;
%p A371458 end proc:
%p A371458 seq(A371458(n),n=0..70) ; # _R. J. Mathar_, Jun 07 2024
%o A371458 (PARI) a(n) = sum(k=0, n\3, 9^k*binomial(n/3-1, k));
%Y A371458 Cf. A362206, A371456.
%Y A371458 Cf. A066872, A098615, A373510, A373511.
%K A371458 nonn
%O A371458 0,5
%A A371458 _Seiichi Manyama_, Jun 07 2024