A024865 - OEIS

%I #7 Sep 08 2022 05:09:38

%S 0,0,1,2,3,0,0,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,

%T 15,17,19,21,23,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,25,

%U 27,29,31,33,35,37,39,41,43,45,47,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,30

%N a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A000027, t = A023533.

%H G. C. Greubel, <a href="/A024865/b024865.txt">Table of n, a(n) for n = 2..5000</a>

%t A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3] != n, 0, 1];

%t A024865[n_]:= A024865[n]= Sum[j*A023533[n-j+1], {j, Floor[n/2]}];

%t Table[A024865[n], {n, 2, 130}] (* _G. C. Greubel_, Sep 07 2022 *)

%o (Magma)

%o A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;

%o A024865:= func< n | (&+[k*A023533(n+1-k): k in [1..Floor(n/2)]]) >;

%o [A024865(n): n in [2..130]]; // _G. C. Greubel_, Sep 07 2022

%o (SageMath)

%o @CachedFunction

%o def A023533(n): return 0 if (binomial( floor( (6*n-1)^(1/3) ) +2, 3) != n) else 1

%o def A024865(n): return sum(k*A023533(n-k+1) for k in (1..(n//2)))

%o [A024865(n) for n in (2..130)] # _G. C. Greubel_, Sep 07 2022

%Y Cf. A000027, A023533.

%K nonn

%O 2,4

%A _Clark Kimberling_