A255849 Characteristic function of pentagonal numbers.

1, 1, 0, 0, 0, 1, 0, 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, 1, 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, 1

Offset

0

Comments

Pentagonal numbers are of the form (3*n^2-n)/2.

Links

Table of n, a(n) for n=0..70.

Index entries for characteristic functions

Formula

For n > 0, a(n) = floor(sqrt(2*n/3+1/36)+1/6)-floor(sqrt(2*(n-1)/3+1/36)+1/6).

Mathematica

Join[{1}, Table[If[IntegerQ[(1+Sqrt[1+24n])/6], 1, 0], {n, 100}]] (* Harvey P. Dale, Feb 25 2018 *)
Module[{nn=20, n5}, n5=PolygonalNumber[5, Range[0, nn]]; Table[If[MemberQ[ n5, n], 1, 0], {n, 0, n5[[-1]]}]] (* Harvey P. Dale, Dec 30 2021 *)

Prog

(PARI) a(n) = ispolygonal(n, 5); \\ Michel Marcus, Aug 04 2023

Crossrefs

Cf. A000326, A080995, A180446.

Sequence in context: A012245 A256436 A253903 * A185059 A179776 A360130

Adjacent sequences: A255846 A255847 A255848 * A255850 A255851 A255852

Keyword

nonn

Author

Mikael Aaltonen, Mar 08 2015

Status

approved