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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 G. C. Greubel, Table of n, a(n) for n = 1..5000 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 Cf. A023531, A023533. Sequence in context: A122179 A335877 A125203 * A321925 A025922 A342322 Adjacent sequences: A023562 A023563 A023564 * A023566 A023567 A023568 KEYWORD nonn AUTHOR Clark Kimberling STATUS approved

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