A024326 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = A023533.
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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Mathematica
nmax = 120; A023533:= A023533 = With[{ms= Table[m(m+1)(m+2)/6, {m, 0, nmax+5}]}, Table[If[MemberQ[ms, n], 1, 0], {n, 0, nmax+5}]]; AbsoluteTiming[Table[t=0; m=3; p=BitShiftRight[n]; n--; While[n>p, t += A023533[[n + 1]]; n -= m++]; t, {n, nmax}]] (* G. C. Greubel, Jan 29 2022 *)
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Sage
nmax=120 @CachedFunction def A023531(n): if ((sqrt(8*n+9) -3)/2).is_integer(): return 1 else: return 0 @CachedFunction def B_list(N): A = [] for m in range(ceil((6*N)^(1/3))): A.extend([0]*(binomial(m+2, 3) -len(A)) +[1]) return A A023533 = B_list(nmax+5) @CachedFunction def A023324(n): return sum( A023531(j)*A023533[n-j+1] for j in (1..((n+1)//2)) ) [A023324(n) for n in (1..nmax)] # G. C. Greubel, Jan 29 2022
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