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Search: id:A096402
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| A096402 |
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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. |
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4
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| 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; listen)
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OFFSET
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1,4
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COMMENT
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The problem of computing the polytope volume was raised by A. N. Kirillov.
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FORMULA
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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)
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EXAMPLE
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f(a,b,1)=a, f(a,b,2)= ab - a^2/2
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CROSSREFS
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Sequence in context: A006216 A047026 A115276 this_sequence A007268 A109156 A129867
Adjacent sequences: A096399 A096400 A096401 this_sequence A096403 A096404 A096405
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KEYWORD
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nonn
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AUTHOR
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R. P. Stanley (rstan(AT)math.mit.edu), Aug 06 2004
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