A005567 Number of walks on square lattice. (Formerly M4723)

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

Offset

0,1

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

Table of n, a(n) for n=0..22.

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

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

N. J. A. Sloane

Status

approved