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Search: id:A132884
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| A132884 |
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Triangle read by rows: T(n,k) is the number of paths in the right-half plane from (0,0) to (n,0), consisting of steps U=(1,1), D=(1,-1), h=(1,0), and H=(2,0), having k h=(1,0) steps (0<=k<=n). |
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+0
1
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| 1, 0, 1, 3, 0, 1, 0, 8, 0, 1, 13, 0, 15, 0, 1, 0, 57, 0, 24, 0, 1, 63, 0, 156, 0, 35, 0, 1, 0, 384, 0, 340, 0, 48, 0, 1, 321, 0, 1380, 0, 645, 0, 63, 0, 1, 0, 2505, 0, 3800, 0, 1113, 0, 80, 0, 1, 1683, 0, 11145, 0, 8855, 0, 1792, 0, 99, 0, 1, 0, 16008, 0, 37065, 0, 18368, 0, 2736, 0
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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T(2n,0)=A001850(n) (the central Delannoy numbers); T(2n+1,0)=0. T(2n,1)=0; T(2n-1,1)=A108666(n). T(n,k)=0 if n+k is odd. Row sums yield A059345. See A132277 for the same statistic on paths restricted to the first quadrant.
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FORMULA
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G.f.=1/sqrt((1-tz-z^2)^2-4z^2).
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EXAMPLE
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Triangle starts:
1;
0,1;
3,0,1;
0,8,0,1;
13,0,15,0,1;
0,57,0,24,0,1;
T(3,1)=8 because we have hH, Hh, hUD, UhD, UDh, hDU, DhU, and DUh.
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MAPLE
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G:=1/sqrt((1-t*z-z^2)^2-4*z^2): Gser:=simplify(series(G, z=0, 15)): for n from 0 to 11 do P[n]:=sort(coeff(Gser, z, n)) end do: for n from 0 to 11 do seq(coeff(P[n], t, j), j=0..n) end do; # yields sequence in triangular form
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CROSSREFS
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Cf. A001850, A108666, A059345, A132277.
Sequence in context: A073278 A135481 A128311 this_sequence A094675 A112743 A119467
Adjacent sequences: A132881 A132882 A132883 this_sequence A132885 A132886 A132887
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 03 2007
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