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Search: id:A133656
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| A133656 |
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Number of below-diagonal paths from (0,0) to (n,n) using steps (1,0), (0,1) and (2k-1,1), k a positive integer. |
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+0
1
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| 1, 2, 6, 23, 99, 456, 2199, 10962, 56033, 292094, 1546885, 8299058, 45010492, 246377362, 1359339710, 7551689783, 42206697209, 237156951618, 1338917298708, 7591380528489, 43207023511013, 246773061257046, 1413889039642479
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Brian Drake, Table of n, a(n) for n = 1..50
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FORMULA
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G.f. g(x) satisfies g(x) = 1 + x*g(x)^2+x*g(x)/(1-x^2*g(x)^2)
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EXAMPLE
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a(4)=99 since there are 90 Schroder paths (A006318) from (0,0) to (4,4) plus DNNEN, DNENN, DENNN, DdNN, DNdN, DNNd, EDNNN, ENDNN and dDNN, where E=(1,0), N=(0,1), D=(3,1) and d=(1,1).
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MAPLE
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A:=series(RootOf(1+_Z*(x-1)+_Z^2*(x-x^2)+_Z^3*x^2-_Z^4*x^3), x, 21): seq(coeff(A, x, i), i=0..20);
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CROSSREFS
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Cf. A006318, A064641, A052709, A063020.
Sequence in context: A150297 A150298 A009449 this_sequence A078487 A120346 A050389
Adjacent sequences: A133653 A133654 A133655 this_sequence A133657 A133658 A133659
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KEYWORD
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easy,nonn
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AUTHOR
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Brian Drake (bdrake(AT)brandeis.edu), Sep 20 2007
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