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 A192365 Number of lattice paths from (0,0) to (n,n) using steps (1,0),(2,0),(0,1),(0,2),(1,1),(2,2). 8
 1, 3, 22, 165, 1327, 10950, 92045, 783579, 6733966, 58294401, 507579829, 4440544722, 39000863629, 343677908223, 3037104558574, 26904952725061, 238854984979423, 2124492829796598, 18927927904130617, 168888613467092895, 1508973226894216106, 13498652154574126523, 120886709687492946083 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.:  ogf^2 = ((2*x^2+6*x-3)/p4 - 2/sqrt(p4))/(4*x^2-4*x-5) where p4 = x^4+6*x^3+7*x^2-10*x+1. - Mark van Hoeij, Apr 16 2013 MAPLE p4 := x^4+6*x^3+7*x^2-10*x+1; ogf := sqrt( ((2*x^2+6*x-3)/p4 - 2/sqrt(p4))/(4*x^2-4*x-5) ); series(ogf, x=0, 30);  # Mark van Hoeij, Apr 16 2013 # second Maple program: b:= proc(x, y) option remember; `if`(min(x, y)<0, 0,       `if`(max(x, y)=0, 1, add(b(x, y-j)+          b(x-j, y)+b(x-j, y-j), j=1..2)))     end: a:= n-> b(n\$2): seq(a(n), n=0..30);  # Alois P. Heinz, May 16 2017 MATHEMATICA b[x_, y_] := b[x, y] = If[Min[x, y] < 0, 0, If[Max[x, y] == 0, 1, Sum[b[x, y - j] + b[x - j, y] + b[x - j, y - j], {j, 1, 2}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 23 2017, after Alois P. Heinz *) PROG (PARI) /* same as in A092566 but use */ steps=[[0, 1], [0, 2], [1, 0], [2, 0], [1, 1], [2, 2]]; /* Joerg Arndt, Jun 30 2011 */ CROSSREFS Sequence in context: A183259 A218668 A164021 * A074578 A290719 A074576 Adjacent sequences:  A192362 A192363 A192364 * A192366 A192367 A192368 KEYWORD nonn AUTHOR Eric Werley, Jun 29 2011 EXTENSIONS Terms >507579829 by Joerg Arndt, Jun 30 2011. STATUS approved

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Last modified September 19 03:31 EDT 2021. Contains 347550 sequences. (Running on oeis4.)