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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)
OFFSET
0,3
COMMENTS
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.
LINKS
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.
FORMULA
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.
EXAMPLE
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.
CROSSREFS
Sequence in context: A113583 A174489 A009563 * A111849 A009159 A013055
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified July 22 15:42 EDT 2024. Contains 374540 sequences. (Running on oeis4.)