A255849 - OEIS

%I #24 Dec 15 2024 17:14:40

%S 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,

%T 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,

%U 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0

%N Characteristic function of pentagonal numbers.

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

%H Antti Karttunen, <a href="/A255849/b255849.txt">Table of n, a(n) for n = 0..101270</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

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

%t Join[{1},Table[If[IntegerQ[(1+Sqrt[1+24n])/6],1,0],{n,100}]] (* _Harvey P. Dale_, Feb 25 2018 *)

%t 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 *)

%o (PARI) a(n) = ispolygonal(n, 5); \\ _Michel Marcus_, Aug 04 2023

%Y Characteristic function of A000326.

%Y Cf. A080995, A180446.

%K nonn

%O 0

%A _Mikael Aaltonen_, Mar 08 2015

%E More terms from _Antti Karttunen_, Dec 15 2024