%I #16 Aug 05 2018 08:23:26
%S 1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 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,
%U 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
%N Characteristic function of icosahedral numbers.
%C Icosahedral numbers are of the form m*(5*m^2 - 5*m + 2)/2.
%H Antti Karttunen, <a href="/A256434/b256434.txt">Table of n, a(n) for n = 0..104160</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F For n > 0, a(n) = floor(t(n) - 1/(45 * t(n)) + 1/3) - floor(t(n-1) - 1/(45 * t(n-1)) + 1/3), where t(n) = ( sqrt(135*n^2-40*n+3)/(15^(3/2)) + (27*n-4)/135 )^(1/3).
%o (PARI)
%o A006564(n) = (5*n^2*(n-1)/2+n); \\ From A006564
%o A256434(n) = { my(i=0); while(A006564(i) < n, i++); return(A006564(i) == n); }; \\ _Antti Karttunen_, Aug 05 2018
%Y Cf. A006564 (icosahedral numbers).
%Y Cf. also A023533, A010057, A256432, A256433.
%K nonn
%O 0
%A _Mikael Aaltonen_, Mar 28 2015
%E More terms from _Antti Karttunen_, Aug 05 2018