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%I M4723 #41 Apr 13 2022 13:25:17
%S 10,70,308,1092,3414,9834,26752,69784,176306,434382,1048812,2490636,
%T 5833006,13500754,30933368,70255008,158335434,354419190,788529700,
%U 1744831060,3841983110,8422163130,18387829488
%N Number of walks on square lattice.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
%H R. K. Guy, <a href="/A005555/a005555.pdf">Letter to N. J. A. Sloane, May 1990</a>
%H R. K. Guy, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/GUY/catwalks.html">Catwalks, sandsteps and Pascal pyramids</a>, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6, (see Figure 6).
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%F a(n) = 26 + 11*n + n^2 + (-16 + 24*n + 8*n^2)*2^n. - Fitted by _John W. Layman_
%p A005567:=2*(5-10*z+4*z**2)/(2*z-1)**3/(z-1)**3; # conjectured by _Simon Plouffe_ in his 1992 dissertation
%o (PARI) a(n) = 26 + 11*n + n^2 + (-16 + 24*n + 8*n^2)*2^n; \\ _Michel Marcus_, Oct 13 2014
%K nonn,walk,easy
%O 0,1
%A _N. J. A. Sloane_
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