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 A192364 Number of lattice paths from (0,0) to (n,n) using steps (0,1),(0,2),(1,0),(2,0),(1,1). 10
 1, 3, 21, 157, 1239, 10047, 82951, 693603, 5854581, 49778997, 425712429, 3657968097, 31555053921, 273109567797, 2370474720369, 20625186298269, 179841473895447, 1571088267426447, 13747953837604959, 120482775658910763, 1057293764707074027, 9289536349244758791, 81709329486947791419 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA From Vaclav Kotesovec, Oct 24 2012: (Start) 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) = A091533(2*n,n) for n >= 0. - Paul D. Hanna, Dec 11 2018 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 MATHEMATICA 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]] PROG (PARI) /* same as in A092566 but use */ steps=[[0, 1], [0, 2], [1, 0], [2, 0], [1, 1]]; /* Joerg Arndt, Jun 30 2011 */ CROSSREFS Cf. A091533. Sequence in context: A226560 A026333 A205773 * A286918 A358953 A189508 Adjacent sequences: A192361 A192362 A192363 * A192365 A192366 A192367 KEYWORD nonn,walk AUTHOR Eric Werley, Jun 29 2011 EXTENSIONS Terms > 425712429 by Joerg Arndt, Jun 30 2011 STATUS approved

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Last modified December 7 11:41 EST 2023. Contains 367656 sequences. (Running on oeis4.)