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A025075
a(n) = s(1)*t(n+1) + s(2)*t(n) + ... + s(k)*t(n-k+2), where k = floor((n+1)/2), s = A023532, t = A023533.
2
0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1
OFFSET
1,34
LINKS
FORMULA
a(n)_= Sum_{k=1..floor((n+1)/2)} A023532(k) * A023533(n-k+2).
MATHEMATICA
A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3]!= n, 0, 1];
A023532[n_]:= If[IntegerQ[(Sqrt[8*n+9] -3)/2], 0, 1];
A025075[n_]:= A025075[n]= Sum[A023532[j]*A023533[n-j+2], {j, Floor[(n+1)/2]}];
Table[A025075[n], {n, 130}] (* G. C. Greubel, Aug 02 2022 *)
PROG
(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
A023532:= func< n | IsSquare(8*n+9) select 0 else 1 >;
A025075:= func< n | (&+[A023532(k)*A023533(n+2-k): k in [1..Floor((n+1)/2)]]) >;
[A025075(n): n in [1..130]]; // G. C. Greubel, Aug 02 2022
(SageMath)
@CachedFunction
def A023533(n): return 0 if (binomial( floor( (6*n-1)^(1/3) ) +2, 3) != n) else 1
def A023532(n): return 0 if is_square(8*n+9) else 1
def A025075(n): return sum(A023532(k)*A023533(n-k+2) for k in (1..((n+1)//2)))
[A025075(n) for n in (1..130)] # G. C. Greubel, Aug 02 2022
CROSSREFS
Sequence in context: A276321 A152196 A024375 * A175609 A038717 A073267
KEYWORD
nonn
STATUS
approved