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A288527
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Number of (undirected) paths in the grid graph P_3 X P_n.
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3
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3, 49, 322, 1618, 7119, 28917, 111360, 412998, 1490095, 5266919, 18329164, 63032354, 214788229, 726753651, 2445603148, 8194841668, 27369348241, 91175639607, 303133174298, 1006289129240, 3336552385073, 11052905264953, 36588907685926, 121056347131508
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = 10*a(n-1)-37*a(n-2)+59*a(n-3)-27*a(n-4)-25*a(n-5)+21*a(n-6)+5*a(n-7)-4*a(n-8)-a(n-9) for n>9.
Empirical g.f.: x*(3 + 19*x - 57*x^2 + 34*x^3 + 43*x^4 - 7*x^5 - 13*x^6 - 2*x^7) / ((1 - x)^3*(1 - 2*x - x^2)^2*(1 - 3*x - x^2)). - Colin Barker, Jun 11 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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