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Search: id:A101347
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| A101347 |
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Triangle read by rows: T(n,k) is the number of k-matchings of the wheel graph W_n. |
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+0
1
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| 1, 1, 1, 1, 4, 1, 6, 3, 1, 8, 10, 1, 10, 20, 5, 1, 12, 33, 20, 1, 14, 49, 49, 7, 1, 16, 68, 96, 34, 1, 18, 90, 165, 99, 9, 1, 20, 115, 260, 225, 52, 1, 22, 143, 385, 440, 176, 11, 1, 24, 174, 544, 777, 456, 74, 1, 26, 208, 741, 1274, 1001, 286, 13, 1, 28, 245, 980, 1974, 1960
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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C. D. Godsil, Algebraic Combinatorics, Chapman & Hall, New York, 1993.
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FORMULA
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T(n, k)=nC(n-k, k)/(n-k)+nC(n-k, k-1) (n>1). G.f.=(1+tz^2)(1-z+tz-tz^2)/(1-z-tz^2)^2.
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EXAMPLE
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T(3,2)=3 because the 2-matchings of the wheel W_3 (triangle ABC with spokes OA,OB,OC) are (AB,OC), (BC, OA), and (CA, OB).
Triangle begins:
1;
1,1;
1,4;
1,6,3;
1,8,10;
1,10,20,5;
1,12,33,20;
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MAPLE
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T:=proc(n, k) if n=0 and k=0 then 1 elif n=1 and k=1 then 1 elif k>ceil(n/2) then 0 else n*binomial(n-k, k)/(n-k)+n*binomial(n-k, k-1) fi end: for n from 0 to 15 do seq(T(n, k), k=0..ceil(n/2)) od; # yields sequence in triangular form
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CROSSREFS
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Row sums yield A061705. T(2n,n)=A005893(n)
Cf. A061705, A005893.
Sequence in context: A098987 A038457 A141649 this_sequence A127556 A050307 A021710
Adjacent sequences: A101344 A101345 A101346 this_sequence A101348 A101349 A101350
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 25 2004
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