The OEIS is supported by the many generous donors to the OEIS Foundation.



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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261747 Chocolate-2 numbers. 3
1, 1, 4, 56, 1712, 92800, 7918592, 984237056, 168662855680, 38238313152512, 11106033743298560, 4026844843819663360, 1784377436257886142464, 949324216111786046259200, 597340801661667138076672000, 438858704839955952346364641280 (list; graph; refs; listen; history; text; internal format)



Given a 2-by-n chocolate bar, a(n) is the number of ways to break it into 2n unit pieces where each break occurs along a gridline. Order matters, and the pieces are distinguishable.

For n>1, a(n) is divisible by 2^n.


Table of n, a(n) for n=0..15.

Caleb Ji, Tanya Khovanova, Robin Park, Angela Song, Chocolate Numbers, arXiv:1509.06093 [math.CO], 2015.

Caleb Ji, Tanya Khovanova, Robin Park, Angela Song, Chocolate Numbers, Journal of Integer Sequences, Vol. 19 (2016), #16.1.7.


a(n) = A(n,2) with A(m,n)=1 for max(m,n)<2 and A(m,n) = Sum_{i=1..m-1} C(m*n-2,i*n-1) *A(i,n) *A(m-i,n) + Sum_{i=1..n-1} C(m*n-2,i*m-1) *A(m,i) *A(m,n-i) else.


For n = 2, there are two ways for the first break: breaking it horizontally or vertically. After that we need two more breaks that can be done in any order. Thus a(2) = 4.


Cf. A257281, A261746, A261964.

Sequence in context: A113583 A174489 A009563 * A111849 A009159 A013055

Adjacent sequences: A261744 A261745 A261746 * A261748 A261749 A261750




Caleb Ji, Tanya Khovanova, Robin Park, Angela Song, Aug 30 2015



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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 19:28 EST 2022. Contains 358648 sequences. (Running on oeis4.)