A256433 - OEIS

%I #16 Aug 05 2018 08:23:34

%S 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,

%T 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,

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

%N Characteristic function of dodecahedral numbers.

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

%H Antti Karttunen, <a href="/A256433/b256433.txt">Table of n, a(n) for n = 0..105995</a>

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

%F 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).

%t 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 *)

%o (PARI)

%o A006566(n) = (n*(3*n-1)*(3*n-2)/2);

%o A256433(n) = { my(i=0); while(A006566(i) < n, i++); return(A006566(i) == n); }; \\ _Antti Karttunen_, Aug 05 2018

%Y Cf. A006566 (dodecahedral numbers).

%Y Cf. also A023533, A010057, A256432, A256434.

%K nonn

%O 0

%A _Mikael Aaltonen_, Mar 28 2015