|
| |
|
|
A096402
|
|
n! times the volume of the polytope x_i >= 0 for 1 <= i <= n and x_i + x_{i+1} + x_{i+2} <= 1 for 1 <= i <= n-2.
|
|
0
|
|
|
|
1, 1, 1, 2, 5, 14, 47, 182, 786, 3774, 19974, 115236, 720038, 4846512, 34950929, 268836776, 2197143724, 19013216102, 173672030192, 1669863067916, 16858620684522, 178306120148144, 1971584973897417, 22748265125187632
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,4
|
|
|
COMMENTS
|
The problem of computing the polytope volume was raised by A. N. Kirillov.
Stanley refers to Exercise-4.56(d) of Enumerative Combinatorics, vol. 1, 2nd ed. in mathoverflow question 87801. - Michael Somos, Feb 07 2012
|
|
|
LINKS
|
Table of n, a(n) for n=1..24.
R. Stanley, A polynomial recurrence involving partial derivatives
|
|
|
FORMULA
|
f(1, 1, n)*n!, where f(a, b, 0)=1, f(0, b, n) = 0 for n>0 and the derivative of f(a, b, n) with respect to a is f(b-a, 1-a, n-1)
a(n) = n! * g(0, 1, n+1) where g(a, b, n) = f(a, b, n)/a. - Michael Somos, Feb 21 2012
|
|
|
EXAMPLE
|
f(a,b,1)=a, f(a,b,2)= ab - a^2/2.
x + x^2 + x^3 + 2*x^4 + 5*x^5 + 14*x^6 + 47*x^7 + 182*x^8 + 786*x^9 +...
|
|
|
CROSSREFS
|
Sequence in context: A149903 A149904 A115276 * A007268 A109156 A143918
Adjacent sequences: A096399 A096400 A096401 * A096403 A096404 A096405
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Richard Stanley, Aug 06 2004
|
|
|
STATUS
|
approved
|
| |
|
|
