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A023533
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a(n) = 1 if n is of the form m(m+1)(m+2)/6, and 0 otherwise.
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63
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1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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a(n) is the characteristic function of tetrahedral numbers. - Mikael Aaltonen, Mar 28 2015
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LINKS
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FORMULA
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For n > 0, a(n) = floor(t(n+1) + 1/(3 * t(n+1)) - 1) - floor(t(n) + 1/(3 * t(n)) - 1), where t(n) = ( sqrt(243*n^2-1)/3^(3/2) + 3*n )^(1/3). - Mikael Aaltonen, Mar 28 2015; corrected by Michel Marcus, Jul 17 2022
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MATHEMATICA
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With[{ms=Table[m(m+1)(m+2)/6, {m, 0, 20}]}, Table[If[MemberQ[ms, n], 1, 0], {n, 0, 100}]] (* Harvey P. Dale, Jul 25 2011 *)
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PROG
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(Sage) # Generates an array with at least N terms.
A = []
for m in range(ceil((6*N)^(1/3))):
A.extend([0]*(binomial(m+2, 3) - len(A)) + [1])
return A
(PARI) lista(nn) = {v = vector(nn); for (n=0, nn, i = 1+n*(n+1)*(n+2)/6; if (i > nn, break); v[i] = 1; ); v; } \\ Michel Marcus, Mar 16 2015
(PARI) a(n) = if(n==0, return(1)); my(t = sqrtnint(6*n-1, 3)); binomial(t+2, 3) == n; \\ Michel Marcus, Jul 19 2022; after A014306
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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