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A256432 Characteristic function of octahedral numbers. 2
1, 1, 0, 0, 0, 0, 1, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0
COMMENTS
Octahedral numbers are of the form (2*n^3 + n)/3.
LINKS
FORMULA
For n > 0, a(n) = floor(t(n) - 1/(6 * t(n))) - floor(t(n-1) - 1/(6 * t(n-1))), where t(n) = ( sqrt(243*n^2+2)/(4*3^(3/2)) + 3*n/4 )^(1/3).
MATHEMATICA
Module[{upto=100, max, oct}, max=(Surd[6, 3](27upto+Sqrt[6+729upto^2])^ (2/3))/ (Surd[6, 3]^2 (27upto+Sqrt[6+729upto^2])^(1/3)); oct=Table[ (2n^3+n)/ 3, {n, 0, max}]; Table[If[MemberQ[oct, k], 1, 0], {k, 0, upto}]] (* Harvey P. Dale, Dec 01 2017 *)
CROSSREFS
Cf. A005900 (octahedral numbers).
Sequence in context: A266253 A113052 A369967 * A218171 A362130 A361018
KEYWORD
nonn
AUTHOR
Mikael Aaltonen, Mar 28 2015
STATUS
approved

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Last modified June 19 17:03 EDT 2024. Contains 373504 sequences. (Running on oeis4.)