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A023565 Convolution of A023531 and A023533. 1
0, 1, 0, 0, 2, 0, 0, 1, 1, 0, 1, 1, 0, 2, 0, 0, 1, 1, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 0, 0, 1, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 3, 0, 0, 2, 0, 0, 1, 1, 0, 2, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
LINKS
FORMULA
a(n) = Sum_{j=1..n} A023533(j) * A023531(n-j+1). - G. C. Greubel, Jul 16 2022
MATHEMATICA
A023531[n_]:= If[IntegerQ[(Sqrt[8*n+9] -3)/2], 1, 0];
A023533[n_]:= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3] != n, 0, 1];
A023565[n_]:= A023565[n]= Sum[A023533[k]*A023531[n-k+1], {k, n}];
Table[A023565[n], {n, 100}] (* G. C. Greubel, Jul 16 2022 *)
PROG
(Magma)
A023531:= func< n | IsIntegral((Sqrt(8*n+9) - 3)/2) select 1 else 0 >;
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[A023533(k)*A023531(n+1-k): k in [1..n]]): n in [1..100]]; // G. C. Greubel, Jul 16 2022
(SageMath)
@CachedFunction
def A023531(n): return 1 if ((sqrt(8*n+9) -3)/2).is_integer() else 0
@CachedFunction
def A023533(n): return 0 if binomial( floor((6*n-1)^(1/3)) +2, 3)!=n else 1
[sum(A023533(k)*A023531(n-k+1) for k in (1..n)) for n in (1..100)] # G. C. Greubel, Jul 16 2022
CROSSREFS
Sequence in context: A122179 A335877 A125203 * A321925 A025922 A342322
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 4 13:38 EST 2024. Contains 370532 sequences. (Running on oeis4.)