A072406 Number of values of k for which C(n,k)-C(n-2,k-1) is odd.

1, 2, 3, 2, 4, 4, 6, 4, 6, 8, 6, 4, 8, 8, 12, 8, 10, 16, 6, 4, 8, 8, 12, 8, 12, 16, 12, 8, 16, 16, 24, 16, 18, 32, 6, 4, 8, 8, 12, 8, 12, 16, 12, 8, 16, 16, 24, 16, 20, 32, 12, 8, 16, 16, 24, 16, 24, 32, 24, 16, 32, 32, 48, 32, 34, 64, 6, 4, 8, 8, 12, 8, 12, 16, 12, 8, 16, 16, 24, 16

Offset

0,2

Links

Table of n, a(n) for n=0..79.

Formula

If 2*2^m+1<n<=3*2^m+1 then a(n)=a(n-2^m) except that a(3*2^m)=a(2^m)+2; if 3*2^m+1<n<=4*2^m+1 then a(n)=2*a(n-2^m) except that a(4*2^m)=2*a(3*2^m)-6. So a(2^m)=2^(m-1)+2, a(2^m+1)=2^m, a(2^m+2)=6, a(2^m+3)=4, a(3*2^m)=2^m+4, a(3*2^m+1)=2^(m+1), a(3*2^m+2)=12, a(3*2^m+3)=8, etc. for m large enough to avoid confusion.

Example

a(5)=4 since the values of C(5,k)-C(3,k-1) are 1-0, 5-1, 10-3, 10-3, 5-1, 1-0, i.e. 1,4,7,7,4,1 of which 4 are odd.

Mathematica

Join[{1, 2}, Table[Count[Table[Binomial[n, k]-Binomial[n-2, k-1], {k, 0, n}], _?OddQ], {n, 2, 80}]] (* Harvey P. Dale, Mar 03 2024 *)

Crossrefs

Cf. A001316, A072405.

Cf. A094959.

Sequence in context: A363263 A153846 A284383 * A297117 A364464 A120680

Adjacent sequences: A072403 A072404 A072405 * A072407 A072408 A072409

Keyword

nonn

Author

Henry Bottomley, Jun 16 2002

Status

approved