A094780 Let 2^k = smallest power of 2 >= binomial(2n,n); a(n) = 2^k - binomial(2n,n).

0, 0, 2, 12, 58, 4, 100, 664, 3514, 16916, 77388, 343144, 1490148, 6376616, 26992264, 113317936, 472661434, 1961361076, 8104733884, 33374212936, 137031378124, 11497939448, 94924291832, 562662294608, 2936768405732, 14326881917576, 67031420473208, 304860388037136

Offset: 0

Author

N. J. A. Sloane, Jun 10 2004

Keywords

• nonn

Comments

Suggested by reading the Knuth article.

Examples

			C(30,15) = 155117520; 2^28 = 268435456; difference is 113317936.
k = 0, 1, 3, 5, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, ... - _R. J. Mathar_, Nov 15 2019
		

References

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

Crossrefs

Cf. A093387, A094779.

Programs

Maple

A094780 := proc(n)
    local cb,k ;
    cb := binomial(2*n,n) ;
    k := ceil(log[2](cb)) ;
    2^k-cb ;
end proc:
seq(A094780(n),n=0..10); # R. J. Mathar, Nov 15 2019