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A023671
Convolution of A023533 and A014306.
1
0, 1, 1, 0, 2, 2, 1, 2, 2, 1, 3, 3, 1, 3, 3, 3, 3, 3, 2, 2, 4, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 3, 5, 5, 3, 4, 5, 5, 5, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 4, 6, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6, 6, 5, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 5, 7, 7, 5, 7, 7, 5
OFFSET
1,5
LINKS
FORMULA
a(n) = Sum_{j=1..n} A023533(n-j+1)*A014306(j).
From G. C. Greubel, Jul 18 2022: (Start)
a(n) = Sum_{j=1..n} A023533(n-j+1)*(1 - A023533(j)).
a(n) = A056556(n) - A023670(n). (End)
MATHEMATICA
A023533[n_]:= If[Binomial[Floor[Surd[6*n-1, 3]] + 2, 3] != n, 0, 1];
A023671[n_]:= A023613[n]= Sum[(1-A023533[k])*A023533[n-k+1], {k, n}];
Table[A023671[n], {n, 100}] (* G. C. Greubel, Jul 18 2022 *)
PROG
(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[(1-A023533(k))*A023533(n+1-k): k in [1..n]]): n in [1..100]]; // G. C. Greubel, Jul 18 2022
(Sage)
@CachedFunction
def A023533(n): return 1 if binomial(floor((6*n-1)^(1/3)) +2, 3)!=n else 0
def A023671(n): return sum((1-A023533(k))*A023533(n-k+1) for k in (1..n))
[A023671(n) for n in (1..100)] # G. C. Greubel, Jul 18 2022
CROSSREFS
KEYWORD
nonn
STATUS
approved