OFFSET
0,5
COMMENTS
For every solution x, binomial(n,x) is 4 times an odd integer.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
V. Shevelev, Binomial predictors, arXiv:0907.3302 [math.NT], 2009.
L. Spiegelhofer, M. Wallner, Divisibility of binomial coefficients by powers of two, arXiv:1710.10884
EXAMPLE
For n=8, there are a(8)=2 solutions, namely x=2 and x=6.
For n=9, there are a(9)=4 solutions, namely x=2, 3, 6 and 7.
MAPLE
MATHEMATICA
a120[n_] := DigitCount[n, 2, 1]; a[n_] := Count[Range[0, n], x_ /; a120[x] + a120[n-x] == a120[n]+2]; Array[a, 90, 0] (* Jean-François Alcover, Jul 10 2017 *)
CROSSREFS
A001316 and A163000 count binomial coefficients with 2-adic valuation 0 and 1. A275012 gives a measure of complexity of these sequences. - Eric Rowland, Mar 15 2017
KEYWORD
nonn,look
AUTHOR
Vladimir Shevelev, Jul 31 2009
EXTENSIONS
Extended beyond a(22), examples added by R. J. Mathar, Jul 08 2009
STATUS
approved