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A094780 Let 2^k = smallest power of 2 >= binomial(2n,n); a(n) = 2^k - binomial(2n,n). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Suggested by reading the Knuth article.

REFERENCES

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

LINKS

Table of n, a(n) for n=0..27.

EXAMPLE

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

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

CROSSREFS

Cf. A093387, A094779.

Sequence in context: A067125 A177782 A005038 * A268594 A100103 A281028

Adjacent sequences:  A094777 A094778 A094779 * A094781 A094782 A094783

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 10 2004

STATUS

approved

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Last modified January 24 16:34 EST 2020. Contains 331207 sequences. (Running on oeis4.)