A324964 a(n) = A000139(n) mod 2; Characteristic function of odd fibbinary numbers (A022341).

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, 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, 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

Offset

0

Comments

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

M. Elder and V. Vatter, Problems and Conjectures presented at the Third International Conference on Permutation Patterns, University of Florida, March 7-11, 2005, arXiv:math/0505504 [math.CO], 2005.

Index entries for characteristic functions

Formula

a(n) = A000035(n)*A085357(n) = A000035(n)*A008966(A005940(1+n)). - Antti Karttunen, Aug 22 2019

Mathematica

Table[Mod[2/((n + 1) (2 n + 1)) Binomial[3 n, n], 2], {n, 0, 100}]
ofnQ[n_]:=With[{lst=If[#[[1]]==0, Nothing, #]&/@Split[IntegerDigits[n, 2]]}, Max[Length/@lst]==1&&Mod[n, 2]==1]; Table[If[ofnQ[n], 1, 0], {n, 0, 110}] (* Harvey P. Dale, Feb 21 2026 *)

Prog

(PARI) a(n)=binomial(3*n, n)*2/((n+1)*(2*n+1)) % 2; \\ Michel Marcus, Apr 02 2019
(PARI) A324964(n) = ((n%2)&&!bitand(n, n<<1)); \\ Antti Karttunen, Aug 22 2019

Crossrefs

Cf. A000035, A000139, A005940, A008966, A039956, A085357, A324917, A324965.

Characteristic function of A022341.

Sequence in context: A122415 A241666 A324539 * A285957 A292273 A379966

Adjacent sequences: A324961 A324962 A324963 * A324965 A324966 A324967

Keyword

nonn

Author

Colin Defant, Mar 21 2019

Extensions

Secondary name and more terms added by Antti Karttunen, Aug 22 2019

Status

approved