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Search: id:A128746
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| A128746 |
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Height of the last peak summed over all skew Dyck paths of semilength n. A skew Dyck path is a path in the first quadrant which begins at the origin, ends on the x-axis, consists of steps U=(1,1)(up), D=(1,-1)(down) and L=(-1,-1)(left) so that up and left steps do not overlap. The length of the path is defined to be the number of its steps. |
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+0
2
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| 1, 5, 22, 94, 401, 1723, 7475, 32749, 144803, 645627, 2900256, 13115820, 59669295, 272918415, 1254314310, 5789850730, 26831078075, 124785337255, 582247766810, 2724905891890, 12787603121195, 60162698218325, 283715348775727
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OFFSET
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1,2
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COMMENT
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a(n)=Sum(A128745(n,k), k=1..n).
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REFERENCES
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E. Deutsch, E. Munarini and S. Rinaldi, Skew Dyck paths (in preparation).
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FORMULA
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G.f.=2z[1+z+sqrt(1-6z+5z^2)]/[1-3z+sqrt(1-6z+5z^2)]^2.
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EXAMPLE
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a(2)=5 because the skew Dyck paths of semilength 2 are UD(UD), U(UD)D and U(UD)L and their last peaks (shown between parentheses) have heights 1, 2 and 2, respectively.
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MAPLE
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G:=2*z*(1+z+sqrt(1-6*z+5*z^2))/(1-3*z+sqrt(1-6*z+5*z^2))^2: Gser:=series(G, z=0, 30): seq(coeff(Gser, z, n), n=1..27);
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CROSSREFS
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Cf. A128745.
Sequence in context: A026672 A049652 A026877 this_sequence A049675 A053154 A141222
Adjacent sequences: A128743 A128744 A128745 this_sequence A128747 A128748 A128749
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 31 2007
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