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 A175934 Number of lattice paths from (0,0) to (n,n) using steps S={(1,0),(0,1),(r,r)|0
 1, 2, 7, 27, 116, 532, 2554, 12675, 64507, 334836, 1765833, 9434779, 50962640, 277839361, 1526834471, 8448751385, 47035469902, 263260232668, 1480527858436, 8361881707770, 47409359120684, 269736194796537, 1539547726712437, 8812663513352489, 50579825742416942, 291012706492224315, 1678146650028389023 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES J. P. S. Kung and A. de Mier, Catalan lattice paths with rook, bishop and spider steps, Journal of Combinatorial Theory, Series A 120 (2013) 379-389. - From N. J. A. Sloane, Dec 27 2012 LINKS FORMULA G.f.: (1-x-x^2-sqrt(x^4+2*x^3-x^2-6*x+1))/(2*x). - Mark van Hoeij, Apr 16 2013 EXAMPLE a(2)=7 because we can reach (2,2) in the following ways: (1,0),(1,0),(0,1),(0,1) (1,0),(0,1),(1,0),(0,1) (1,0),(0,1),(1,1) (1,0),(1,1),(0,1)(1,1),(1,0),(0,1) (1,1),(1,1) (2,2) PROG sage: (replace dots with spaces) n=20 M=[] for posx in range(0, n+1): ........for posy in range(0, n+1): ............if posx==0: ................if posy==0: ....................M.append([1]) ................else: ....................M.append([0]) ............else: ................if posy==0: ....................M[0].append(0) ....................M[0][posx]=M[0][posx]+M[0][posx-1] ................else: ....................if posy>posx: ........................M[posy].append(0) ....................else: ........................M[posy].append(0) ........................M[posy][posx]=M[posy][posx-1]+M[posy][posx] ........................M[posy][posx]=M[posy-1][posx]+M[posy][posx] ........................for r in range(1, min(posx, posy, 2)+1): ............................M[posy][posx]=M[posy-r][posx-r]+M[posy][posx] L=[] for k in range(0, n+1): ....L.append(M[k][k]) print L CROSSREFS Cf. A175935, A175936, A175937, A175939. Sequence in context: A150638 A150639 A150640 * A150641 A150642 A150643 Adjacent sequences:  A175931 A175932 A175933 * A175935 A175936 A175937 KEYWORD nonn AUTHOR Eric Werley, Dec 06 2010 STATUS approved

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