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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

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Last modified December 21 23:06 EST 2014. Contains 252326 sequences.