|
Search: id:A103209
|
|
|
| A103209 |
|
Square array T(n,d) read by antidiagonals: number of structurally-different guillotine partitions of a d-dimensional box in R^d by n hyperplanes. |
|
+0
12
|
|
| 1, 1, 2, 1, 6, 3, 1, 22, 15, 4, 1, 90, 93, 28, 5, 1, 394, 645, 244, 45, 6, 1, 1806, 4791, 2380, 505, 66, 7, 1, 8558, 37275, 24868, 6345, 906, 91, 8, 1, 41586, 299865, 272188, 85405, 13926, 1477, 120, 9, 1, 206098, 2474025, 3080596, 1204245, 229326, 26845
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
The columns are the row sums of the inverses of the Riordan arrays ((1-d*x)/(1-x),x(1-d*x)/(1-x)), that is, of the Riordan arrays ((1+x-sqrt(1+2(1-2*d)x+x^2)/(2*d*x),(1+x-sqrt(1+2(1-2*d)x+x^2)/(2*d)). - Paul Barry (pbarry(AT)wit.ie), May 24 2005
|
|
LINKS
|
E. Ackerman, G. Barequet, R. Y. Pinter and D. Romik, The number of guillotine partitions in d dimensions
|
|
FORMULA
|
T(n, d) = (1/n) * Sum[i=0..n-1, C(n, i)*C(n, i-1)*(d-1)^i*d^(n-i) ], T(n, 0)=1.
G.f. of d-th column: [1-z-(z^2-4dz+2z+1)^(1/2)]/(2dz-2z).
T(n, k)=sum{j=0..n, C(n+j, 2j)k^j*C(j)}, C(n) as in A000108. - Paul Barry (pbarry(AT)wit.ie), May 21 2005
|
|
EXAMPLE
|
1,...1,....1,.....1,......1,......1,.......1,.......1,.......1,
1,...2,....3,.....4,......5,......6,.......7,.......8,.......9,
1,...6,...15,....28,.....45,.....66,......91,.....120,.....153,
1,..22,...93,...244,....505,....906,....1477,....2248,....3249,
1,..90,..645,..2380,...6345,..13926,...26845,...47160,...77265,
1,.394,.4791,.24868,..85405,.229326,..522739,.1059976,.1968633,
1,1806,37275,272188,1204245,3956106,10663471,24958200,52546473,
|
|
CROSSREFS
|
Second column is A006318 (Schroeder numbers), others are A103210 and A103211. Main diagonal is A103212.
Sequence in context: A060539 A163269 A103905 this_sequence A089900 A138533 A096334
Adjacent sequences: A103206 A103207 A103208 this_sequence A103210 A103211 A103212
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Ralf Stephan, Jan 27 2005
|
|
|
Search completed in 0.002 seconds
|
