A256432 Characteristic function of octahedral numbers.

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

Offset

0

Comments

Octahedral numbers are of the form (2*n^3 + n)/3.

Links

Table of n, a(n) for n=0..85.

Index entries for characteristic functions

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

Adjacent sequences: A256429 A256430 A256431 * A256433 A256434 A256435

Keyword

nonn

Author

Mikael Aaltonen, Mar 28 2015

Status

approved