|
%I #23 Aug 22 2019 20:35:09
%S 0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,
%T 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
%U 0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N a(n) = A000139(n) mod 2; Characteristic function of odd fibbinary numbers (A022341).
%C Equals 1 if and only if the binary expansion of n does not contain two 1's in consecutive positions and ends in a 1.
%H Antti Karttunen, <a href="/A324964/b324964.txt">Table of n, a(n) for n = 0..65537</a>
%H M. Elder and V. Vatter, <a href="https://arxiv.org/abs/math/0505504">Problems and Conjectures presented at the Third International Conference on Permutation Patterns, University of Florida, March 7-11, 2005</a>, arXiv:math/0505504 [math.CO], 2005.
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = A000035(n)*A085357(n) = A000035(n)*A008966(A005940(1+n)). - _Antti Karttunen_, Aug 22 2019
%t Table[Mod[2/((n + 1) (2 n + 1)) Binomial[3 n, n], 2], {n, 0, 100}]
%o (PARI) a(n)=binomial(3*n, n)*2/((n+1)*(2*n+1)) % 2; \\ _Michel Marcus_, Apr 02 2019
%o (PARI) A324964(n) = ((n%2)&&!bitand(n,n<<1)); \\ _Antti Karttunen_, Aug 22 2019
%Y Cf. A000035, A000139, A005940, A008966, A039956, A085357, A324917, A324965.
%Y Characteristic function of A022341.
%K nonn
%O 0
%A _Colin Defant_, Mar 21 2019
%E Secondary name and more terms added by _Antti Karttunen_, Aug 22 2019
|
