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A023533 a(n) = 1 if n is of the form m(m+1)(m+2)/6, and 0 otherwise. 41
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is the characteristic function of tetrahedral numbers. - Mikael Aaltonen, Mar 28 2015

LINKS

Danny Rorabaugh, Table of n, a(n) for n = 0..10000

Index entries for characteristic functions

FORMULA

a(A000292(n))=1; a(A145397(n))=0; a(n)=1-A014306(n). - Reinhard Zumkeller, Oct 14 2008

For n > 0, a(n) = floor(t(n) + 1/(3 * t(n)) - 1) - floor(t(n-1) + 1/(3 * t(n-1)) - 1), where t(n) = ( sqrt(243*n^2-1)/3^(3/2) + 3*n )^(1/3). - Mikael Aaltonen, Mar 28 2015

MATHEMATICA

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 *)

PROG

(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])

# Danny Rorabaugh, Mar 16 2015

(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

CROSSREFS

Cf. A000292, A014306, A145397.

Sequence in context: A214505 A127692 A014305 * A010052 A039985 A127239

Adjacent sequences:  A023530 A023531 A023532 * A023534 A023535 A023536

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 14 1998

STATUS

approved

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Last modified August 22 12:50 EDT 2017. Contains 290948 sequences.