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Search: id:A062154
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| A062154 |
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Number T(n,m) of n X m matrices over {0,1,2} with all row and column sums equal to 1 or 2, m=0,..,2*n. |
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+0
3
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| 1, 0, 2, 1, 0, 1, 13, 18, 6, 0, 0, 18, 189, 450, 360, 90, 0, 0, 6, 450, 4842, 16380, 22140, 12600, 2520, 0, 0, 0, 360, 16380, 190080, 832950, 1631700, 1537200, 680400, 113400, 0, 0, 0, 90, 22140, 832950, 10520010, 56609280, 147533400, 200377800
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OFFSET
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0,3
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(Problem 3.4.15).
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FORMULA
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Sum_{n >= 0, m >= 0} T(n, m)*x^n/n!*y^m/m! = 1/sqrt(1-x*y)*exp(x*y/2+1/(1-x*y)*(x*y+x^2*y/2+x*y^2/2)).
Sum_{n >= 0, m >= 0} T(n, m)*x^n/n!*y^m/m! = 1+(1/2*y^2+2*y)*x+(1/8*y^4+3/2*y^3+13/4*y^2+1/2*y)*x^2+(1/48*y^6+1/2*y^5+25/8*y^4+21/4*y^3+3/2*y^2)*x^3+...
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EXAMPLE
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[1], [0, 2, 1], [0, 1, 13, 18, 6], [0, 0, 18, 189, 450, 360, 90], [0, 0, 6, 450, 4842, 16380, 22140, 12600, 2520], [0, 0, 0, 360, 16380, 190080, 832950, 1631700, 1537200, 680400, 113400], [0, 0, 0, 90, 22140, 832950, 10520010, 56609280, 147533400, 200377800, 144585000, 52390800, 7484400], ...
T(2, 2)=13, i.e. there are 13 2 X 2 matrices over {0, 1, 2) with all row and column sums equal to 1 or 2: [0 1 / 0 1], [0 1 / 0 2], [0 2 / 1 0], [1 0 / 1 0], [1 1 / 1 1], [1 1 / 2 0], [2 0 / 1 0], [1 1 / 2 0], [1 0 / 2 0], [0 1 / 0 2], [1 1 / 0 1], [1 0 / 1 1], [0 1 / 0 2].
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CROSSREFS
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Row sums: A062155, A062156.
Sequence in context: A076422 A058998 A085324 this_sequence A110399 A112214 A112608
Adjacent sequences: A062151 A062152 A062153 this_sequence A062155 A062156 A062157
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 06 2001
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