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Search: id:A127618
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| A127618 |
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Number of walks from (0,0) to (n,n) in the region 0 <= x-y <= 4 with the steps (1,0), (0, 1), (2,0) and (0,2). |
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+0
4
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| 1, 1, 5, 22, 117, 590, 3018, 15378, 78440, 399992, 2039852, 10402480, 53049048, 270531368, 1379614800, 7035549312, 35878823312, 182969359520, 933079279328, 4758375627808, 24266039468160, 123748253080832, 631072497876672
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Arvind Ayyer and Doron Zeilberger, The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team was never losing but also never ahead by more than w Points
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FORMULA
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G.f.: (1-3x-5x^2-2x^3+x^4)/(1-4x-6x^2+2x^3)
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EXAMPLE
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a(2)=5 because we can reach (2,2) in the following ways:
(0,0),(1,0),(1,1),(2,1),(2,2)
(0,0),(2,0),(2,2)
(0,0),(1,0),(2,0),(2,2)
(0,0),(2,0),(2,1),(2,2)
(0,0),(1,0),(2,0),(2,1),(2,2)
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CROSSREFS
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Cf. A000108, A046717, A122951, A127617, A127619, A127620.
Adjacent sequences: A127615 A127616 A127617 this_sequence A127619 A127620 A127621
Sequence in context: A008485 A082297 A005033 this_sequence A127619 A127620 A122951
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KEYWORD
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nonn
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AUTHOR
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Arvind Ayyer (ayyer(AT)physics.rutgers.edu), Jan 20 2007
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