A275012 Number of nonzero coefficients in the polynomial factor of the expression counting binomial coefficients with 2-adic valuation n.

1, 1, 4, 11, 29, 69, 174, 413, 995, 2364, 5581, 13082, 30600, 71111, 164660, 379682, 872749

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Eric Rowland, Binomial Coefficients, Valuations, and Words, In: Charlier É., Leroy J., Rigo M. (eds) Developments in Language Theory, DLT 2017, Lecture Notes in Computer Science, vol 10396.

Lukas Spiegelhofer and Michael Wallner, An explicit generating function arising in counting binomial coefficients divisible by powers of primes, arXiv:1604.07089 [math.NT], 2016.

Lukas Spiegelhofer and Michael Wallner, Divisibility of binomial coefficients by powers of two, arXiv:1710.10884 [math.NT], 2017.

Example

For n=2, the number of integers m such that binomial(k,m) is divisible by 2^n but not by 2^(n+1) is given by 2^X_1 (-1/8 X_10 + 1/8 X_10^2 + X_100 + 1/4 X_110), where X_w is the number of occurrences of the word w in the binary representation of k. The polynomial factor of this expression has a(2) = 4 nonzero terms. - Eric Rowland, Mar 05 2017

Crossrefs

A001316, A163000, and A163577 count binomial coefficients with 2-adic valuation 0, 1, and 2. - Eric Rowland, Mar 15 2017

Sequence in context: A000604 A153876 A036881 * A055418 A062432 A220018

Adjacent sequences: A275009 A275010 A275011 * A275013 A275014 A275015

Keyword

nonn,more

Author

Michel Marcus, Nov 12 2016

Extensions

a(12)-a(16) from Eric Rowland, Mar 20 2017

Status

approved