cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A275012 #33 Jun 06 2021 09:05:57
%S A275012 1,1,4,11,29,69,174,413,995,2364,5581,13082,30600,71111,164660,379682,
%T A275012 872749
%N A275012 Number of nonzero coefficients in the polynomial factor of the expression counting binomial coefficients with 2-adic valuation n.
%H A275012 Eric Rowland, <a href="https://dx.doi.org/10.1007/978-3-319-62809-7_3">Binomial Coefficients, Valuations, and Words</a>, In: Charlier É., Leroy J., Rigo M. (eds) Developments in Language Theory, DLT 2017, Lecture Notes in Computer Science, vol 10396.
%H A275012 Lukas Spiegelhofer and Michael Wallner, <a href="https://arxiv.org/abs/1604.07089">An explicit generating function arising in counting binomial coefficients divisible by powers of primes</a>, arXiv:1604.07089 [math.NT], 2016.
%H A275012 Lukas Spiegelhofer and Michael Wallner, <a href="https://arxiv.org/abs/1710.10884">Divisibility of binomial coefficients by powers of two</a>, arXiv:1710.10884 [math.NT], 2017.
%e A275012 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
%Y A275012 A001316, A163000, and A163577 count binomial coefficients with 2-adic valuation 0, 1, and 2. - _Eric Rowland_, Mar 15 2017
%K A275012 nonn,more
%O A275012 0,3
%A A275012 _Michel Marcus_, Nov 12 2016
%E A275012 a(12)-a(16) from _Eric Rowland_, Mar 20 2017