A005567 Number of walks on square lattice.

10, 70, 308, 1092, 3414, 9834, 26752, 69784, 176306, 434382, 1048812, 2490636, 5833006, 13500754, 30933368, 70255008, 158335434, 354419190, 788529700, 1744831060, 3841983110, 8422163130, 18387829488

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• easy

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; arXiv:0911.4975 [math.NT], 2009.
• Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Programs

Maple

A005567:=2*(5-10*z+4*z**2)/(2*z-1)**3/(z-1)**3; # conjectured by Simon Plouffe in his 1992 dissertation

PARI

a(n) = 26 + 11*n + n^2 + (-16 + 24*n + 8*n^2)*2^n; \\ Michel Marcus, Oct 13 2014

Formula

a(n) = 26 + 11*n + n^2 + (-16 + 24*n + 8*n^2)*2^n. - Fitted by John W. Layman