A025126 - OEIS

%I #9 Sep 15 2022 06:24:20

%S 1,1,0,1,1,1,2,2,1,2,2,1,2,2,2,2,2,2,2,3,3,2,3,3,3,3,3,2,3,3,3,3,3,2,

%T 3,3,2,3,4,4,4,4,3,4,4,4,4,4,4,4,4,4,3,4,3,4,4,3,4,4,4,4,4,3,4,4,4,4,

%U 5,5,5,5,5,4,5,5,5,5,5,5,5,5,4,5,5,4,5,5,4,5,5,4,5,5,5,5,5,5,5,5,5,4,5,5,5,5,5,5,5,5,6

%N a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A023533, t = A014306.

%H G. C. Greubel, <a href="/A025126/b025126.txt">Table of n, a(n) for n = 1..5000</a>

%t b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2,3]], {m,0,15}];

%t A025126[n_]:= A025126[n]= Sum[(1-b[j+1])*b[n-j+1], {j, Floor[(n+2)/2], n}];

%t Table[A025126[n], {n,130}] (* _G. C. Greubel_, Sep 14 2022 *)

%o (Magma)

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

%o A025126:= func< n | (&+[(1-A023533(n+2-k))*A023533(k): k in [1..Floor((n+1)/2)]]) >;

%o [A025126(n): n in [1..130]]; // _G. C. Greubel_, Sep 14 2022

%o (SageMath)

%o @CachedFunction

%o def b(j): return sum(bool(j==binomial(m+2,3)) for m in (0..15))

%o @CachedFunction

%o def A025126(n): return sum((1-b(j+1))*b(n-j+1) for j in (((n+2)//2)..n))

%o [A025126(n) for n in (1..130)] # _G. C. Greubel_, Sep 14 2022

%Y Cf. A014306, A023533.

%Y Cf. A024693. [From _R. J. Mathar_, Oct 23 2008]

%K nonn

%O 1,7

%A _Clark Kimberling_