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A192364
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Number of lattice paths from (0,0) to (n,n) using steps (0,1),(0,2),(1,0),(2,0),(1,1).
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10
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1, 3, 21, 157, 1239, 10047, 82951, 693603, 5854581, 49778997, 425712429, 3657968097, 31555053921, 273109567797, 2370474720369, 20625186298269, 179841473895447, 1571088267426447, 13747953837604959, 120482775658910763, 1057293764707074027, 9289536349244758791, 81709329486947791419
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (3 - 6*x + sqrt(-1 + 4*x*(9*x-11) + 4*sqrt(1-x)*sqrt(5+4*x)*sqrt(9*x-1))) / (sqrt(10+8*x)*sqrt((1-x)*(1-9*x))*(4*x*(9*x-11)-1+4*sqrt(1-x)*sqrt(5+4*x)*sqrt(9*x-1))^(1/4))
D-finite with recurrence: 15*(n-1)*n*a(n) = (n-1)*(133*n-54)*a(n-1) + (31*n^2 - 177*n + 224)*a(n-2) - (113*n^2 - 295*n + 144)*a(n-3) - 18*(n-3)*(2*n-5)*a(n-4)
a(n) ~ 3^(2*n+3/2)/(2*sqrt(14*Pi*n))
(End)
a(n) = [x^n*y^n] 1/(1 - x - y - x^2 - x*y - y^2) for n >= 0. - Paul D. Hanna, Dec 11 2018
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MATHEMATICA
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FullSimplify[CoefficientList[Series[(3-6*x+Sqrt[-1+4*x*(9*x-11)+4*Sqrt[1-x]*Sqrt[5+4*x]*Sqrt[9*x-1]])/(Sqrt[10+8*x]*Sqrt[(1-x)*(1-9*x)]*(4*x*(9*x-11)-1+4*Sqrt[1-x]*Sqrt[5+4*x]*Sqrt[9*x-1])^(1/4)), {x, 0, 10}], x]]
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PROG
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(PARI) /* same as in A092566 but use */
steps=[[0, 1], [0, 2], [1, 0], [2, 0], [1, 1]];
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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