A334209 Number of solutions to n = i+j, 0 <= i,j <= n for which A010060(i)=A010060(j)=0, i != j.

0, 0, 2, 0, 2, 2, 0, 2, 4, 2, 2, 4, 2, 2, 8, 2, 4, 6, 2, 6, 6, 4, 8, 6, 4, 6, 10, 4, 10, 10, 0, 10, 12, 6, 10, 10, 6, 8, 16, 8, 8, 12, 10, 10, 14, 12, 8, 14, 12, 10, 18, 10, 14, 16, 8, 14, 20, 14, 10, 20, 10, 10, 32, 10, 12, 22, 10, 18, 22, 16, 16, 20, 16, 16

Offset

1,3

Comments

This is the same as the number of solutions to n = i+j, 0 <= i,j <= n for which A010060(i)=A010060(j)=1, i != j.

Links

Table of n, a(n) for n=1..74.

J. Lambek and L. Moser, On some two way classifications of integers, Can. Math. Bull 2 (1959) 85-89.

Formula

We have

a(4n+1) = -a(2n)+a(2n+1)+a(4n)

a(4n+2) = a(2n)+a(2n+1)

a(8n) = 3a(2n)+a(2n+1)

a(8n+3) = 3a(2n)+a(2n+1)-a(4n)+a(4n+3)

a(8n+4) = a(2n+1)+a(4n)

a(8n+7) = 4a(2n+1),

which provides a fast algorithm to compute a(n).

Example

For n = 19 the only solutions are (i,j) in {(9,10), (10,9)}, so a(19) = 2.

Crossrefs

Cf. A010060.

Sequence in context: A035692 A308654 A329860 * A143613 A208955 A121363

Adjacent sequences: A334206 A334207 A334208 * A334210 A334211 A334212

Keyword

nonn

Author

Jeffrey Shallit, Apr 18 2020

Status

approved