

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 <= n2.


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
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OFFSET

1,4


COMMENTS

The problem of computing the polytope volume was raised by A. N. Kirillov.
Stanley refers to Exercise4.56(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(ba, 1a, n1)
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



