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Search: id:A101350
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| A101350 |
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Triangle read by rows: T(n,k)=number of k-matchings in the graph obtained by a zig-zag triangulation of a convex n-gon, T(0,0)=T(1,0)=T(2,0)=T(2,1)=1 (n>2,0<=k<=floor(n/2)). |
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+0
1
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| 1, 1, 1, 1, 1, 3, 1, 5, 2, 1, 7, 7, 1, 9, 16, 3, 1, 11, 29, 15, 1, 13, 46, 43, 5, 1, 15, 67, 95, 30, 1, 17, 92, 179, 104, 8, 1, 19, 121, 303, 271, 58, 1, 21, 154, 475, 591, 235, 13, 1, 23, 191, 703, 1140, 705, 109, 1, 25, 232, 995, 2010, 1746, 506, 21, 1, 27, 277, 1359, 3309, 3780
(list; graph; listen)
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OFFSET
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0,6
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FORMULA
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G.f.=1/(1-z-tz^2-tz^3-t^2z^4).
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EXAMPLE
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T(5,2)=7 because in the triangulation of the convex pentagon ABCDEA with diagonals AD and AC we have seven 2-matchings: {AB,CD},{AB,DE},{BC,AD},{BC,DE},{BC,EA},{CD,EA}, and {DE,AC}.
Triangle begins:
1;
1;
1,1;
1,3;
1,5,2;
1,7,7;
1,9,16,3;
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MAPLE
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G:=1/(1-z-t*z^2-t*z^3-t^2*z^4):Gserz:=simplify(series(G, z=0, 18)):P[0]:=1: for n from 1 to 16 do P[n]:=sort(coeff(Gserz, z^n)) od:for n from 0 to 16 do seq(coeff(t*P[n], t^k), k=1..1+floor(n/2)) od; # yields the sequence in triangular form
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CROSSREFS
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Row sums yield A000078 (the tetranacci numbers). T(2n+1,n)=A023610(n) (n>0). T(2n,n)=A000045(n+1) (the Fibonacci numbers).
Cf. A000078, A023610, A000045.
Sequence in context: A130323 A130303 A100898 this_sequence A134867 A102573 A134033
Adjacent sequences: A101347 A101348 A101349 this_sequence A101351 A101352 A101353
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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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