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A275012 Number of nonzero coefficients in the polynomial factor of the expression counting binomial coefficients with 2-adic valuation n. 3
1, 1, 4, 11, 29, 69, 174, 413, 995, 2364, 5581, 13082, 30600, 71111, 164660, 379682, 872749 (list; graph; refs; listen; history; text; internal format)



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

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


For n=2, the number of integers m such that binomial(k,m) is divisible by 2^n but not 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


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




Michel Marcus, Nov 12 2016


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



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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)