login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A163577 Count of indices x in [0,n] that satisfy the equation A000120(x) + A000120(n-x) = A000120(n) + 2. 4
0, 0, 0, 0, 2, 0, 1, 0, 2, 4, 1, 0, 5, 2, 2, 0, 2, 4, 5, 8, 5, 2, 4, 0, 5, 10, 4, 4, 10, 4, 4, 0, 2, 4, 5, 8, 9, 10, 12, 16, 5, 10, 6, 4, 12, 8, 8, 0, 5, 10, 12, 20, 12, 8, 12, 8, 10, 20, 8, 8, 20, 8, 8, 0, 2, 4, 5, 8, 9, 10, 12, 16, 9, 18, 14, 20, 20, 24, 24, 32, 5, 10, 14, 20, 14, 12, 16, 8, 12, 24 (list; graph; refs; listen; history; text; internal format)
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

read("transforms") ; A000120 := proc(n) wt(n) ; end:

A163577 := proc(n) local a, x ; a := 0 ; for x from 0 to n do if A000120(x)+A000120(n-x) = A000120(n)+2 then a := a+1; fi; od: a; end:

seq(A163577(n), n=0..130) ; # R. J. Mathar, Jul 08 2009

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

Cf. A000120, A007814.

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

Sequence in context: A030010 A321297 A343156 * A132178 A039655 A103775

Adjacent sequences:  A163574 A163575 A163576 * A163578 A163579 A163580

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)