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A006191
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Number of paths on square lattice.
(Formerly M1490)
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2
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1, 2, 5, 16, 54, 180, 595, 1964, 6485, 21418, 70740, 233640, 771661, 2548622, 8417525, 27801196, 91821114, 303264540, 1001614735, 3308108744, 10925940965, 36085931638, 119183735880, 393637139280, 1300095153721, 4293922600442
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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H. L. Abbott and D. Hanson, A lattice path problem, Ars Combin., 6 (1978), 163-178.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3) + a(n-4) for n>4.
G.f.: x*(1 - 2*x) / ((1 - x + x^2)*(1 - 3*x - x^2)).
(End)
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MATHEMATICA
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LinearRecurrence[{4, -3, 2, 1}, {1, 2, 5, 16}, 30] (* Harvey P. Dale, Mar 22 2018 *)
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CROSSREFS
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KEYWORD
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nonn,walk,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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