A256433 Characteristic function of dodecahedral numbers.

1, 1, 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, 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

Dodecahedral numbers are of the form m(3m-1)(3m-2)/2.

Links

Antti Karttunen, Table of n, a(n) for n = 0..105995

Index entries for characteristic functions

Formula

For n > 0, a(n) = floor(t(n) + 1/(27 * t(n)) + 1/3) - floor(t(n-1) + 1/(27 * t(n-1)) + 1/3), where t(n) = ( sqrt(243*n^2-1)/(3^(9/2)) + n/9 )^(1/3).

For n>0, a(n) = 1 if n==m*(3*m-1)*(3*m-2)/2 and a(n) = 0 otherwise where m = floor((2*n/9)^(1/3))+1. - Chai Wah Wu, Oct 02 2025

Mathematica

With[{ddn=Table[m(3m-1)(3m-2)/2, {m, 0, 10}]}, Table[If[MemberQ[ddn, n], 1, 0], {n, 0, 100}]] (* Harvey P. Dale, Oct 18 2015 *)

Prog

(PARI)
A006566(n) = (n*(3*n-1)*(3*n-2)/2);
A256433(n) = { my(i=0); while(A006566(i) < n, i++); return(A006566(i) == n); }; \\ Antti Karttunen, Aug 05 2018
(Python)
from sympy import integer_nthroot
def A256433(n): return int((m:=integer_nthroot((k:=n<<1)//9, 3)[0]+1)*(3*m-1)*(3*m-2)==k) if n else 1 # Chai Wah Wu, Oct 02 2025

Crossrefs

Cf. A006566 (dodecahedral numbers).

Cf. also A023533, A010057, A256432, A256434.

Sequence in context: A292547 A014032 A014055 * A014028 A014047 A016411

Adjacent sequences: A256430 A256431 A256432 * A256434 A256435 A256436

Keyword

nonn

Author

Mikael Aaltonen, Mar 28 2015

Status

approved