A102395 A mod 2 related Jacobsthal sequence.

1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 6, 0, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 6, 2, 6, 6, 10, 0, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 6, 2, 6, 6, 10, 2, 2, 2, 6, 2, 6, 6, 10, 2, 6, 6, 10, 6, 10, 10, 22, 0, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 6, 2, 6, 6, 10, 2, 2, 2, 6, 2, 6, 6, 10, 2, 6, 6, 10, 6, 10, 10, 22, 2, 2, 2

Offset

0,4

Comments

Conjecture: all the terms are in A078008.

The conjecture is true since a(n) = A078008(A000120(n)). - Paul Barry, Jan 07 2005

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

a(2^n-1) = A078008(n).

A001316(n) = a(n) + 2*A102396(n).

a(n) = Sum_{k=0..n} if(n+k == 0 (mod 3), C(n, k) mod 2, 0).

a(n) = Sum_{k=0..n} (1-ceiling((n+k)/3)+floor((n+k)/3))*(binomial(n,k) mod 2). - Wesley Ivan Hurt, Mar 01 2023

Mathematica

f[n_] := (2^n + 2*(-1)^n)/3; a[n_] := f[DigitCount[n, 2, 1]]; Array[a, 100, 0] (* Amiram Eldar, Jul 22 2023 *)

Crossrefs

Cf. A000120, A078008, A001316, A102396.

Sequence in context: A044943 A292118 A277486 * A127504 A321665 A329321

Adjacent sequences: A102392 A102393 A102394 * A102396 A102397 A102398

Keyword

easy,nonn

Author

Paul Barry, Jan 06 2005

Status

approved