A094779 Let 2^k = smallest power of 2 >= binomial(n,[n/2]); a(n) = 2^k - binomial(n,[n/2]).

0, 0, 0, 1, 2, 6, 12, 29, 58, 2, 4, 50, 100, 332, 664, 1757, 3514, 8458, 16916, 38694, 77388, 171572, 343144, 745074, 1490148, 3188308, 6376616, 13496132, 26992264, 56658968, 113317936, 236330717, 472661434, 980680538, 1961361076, 4052366942, 8104733884

Offset

0,5

Comments

Suggested by reading the Knuth article.

a(n+1) < a(n) for n = 8, 40, 162, 650... - Ivan Neretin, Jun 25 2015

References

D. E. Knuth, Efficient balanced codes, IEEE Trans. Inform. Theory, 32 (No. 1, 1986), 51-53.

Links

Ivan Neretin, Table of n, a(n) for n = 0..1000

Example

C(30,15) = 155117520; 2^28 = 268435456; difference is 113317936.

Mathematica

Table[-(b = Binomial[n, Quotient[n, 2]]) + 2^Ceiling[Log2[b]], {n, 0, 36}] (* Ivan Neretin, Jun 25 2015 *)

Crossrefs

Cf. A093387, A094780.

Sequence in context: A330455 A183467 A057582 * A093387 A324408 A229487

Adjacent sequences: A094776 A094777 A094778 * A094780 A094781 A094782

Keyword

nonn

Author

N. J. A. Sloane, Jun 10 2004

Status

approved