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 A005567 Number of walks on square lattice. (Formerly M4723) 1
 10, 70, 308, 1092, 3414, 9834, 26752, 69784, 176306, 434382, 1048812, 2490636, 5833006, 13500754, 30933368, 70255008, 158335434, 354419190, 788529700, 1744831060, 3841983110, 8422163130, 18387829488 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. LINKS R. K. Guy, Letter to N. J. A. Sloane, May 1990 R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6, (see Figure 6). Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. FORMULA a(n) = 26 + 11*n + n^2 + (-16 + 24*n + 8*n^2)*2^n. - Fitted by John W. Layman MAPLE A005567:=2*(5-10*z+4*z**2)/(2*z-1)**3/(z-1)**3; # conjectured by Simon Plouffe in his 1992 dissertation PROG (PARI) a(n) = 26 + 11*n + n^2 + (-16 + 24*n + 8*n^2)*2^n; \\ Michel Marcus, Oct 13 2014 CROSSREFS Sequence in context: A090084 A025221 A271040 * A174434 A073391 A002802 Adjacent sequences:  A005564 A005565 A005566 * A005568 A005569 A005570 KEYWORD nonn,walk,easy AUTHOR STATUS approved

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Last modified February 28 08:28 EST 2020. Contains 332323 sequences. (Running on oeis4.)