%I M1621 N0634 #36 Dec 27 2019 17:46:50
%S 2,6,18,50,142,390,1086,2958,8134,22050,60146,162466,440750,1187222,
%T 3208298,8622666,23233338,62329366,167558310,448848582,1204403014,
%U 3222280242,8633306906,23073198658,61740677454,164856393110,440658745814
%N Number of n-step walks on square lattice.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Hugo Pfoertner, <a href="/A002900/b002900.txt">Table of n, a(n) for n = 1..79</a>
%F a(n) = (1/2) * A001411(n).
%t (* b = A001411 *) mo = Tuples[{-1, 1}, 2]; b[0] = 1; b[tg_, p_:{{0, 0}}] := b[tg, p] = Block[{e, mv = Complement[Last[p] + #& /@ mo, p]}, If[tg == 1, Length[mv], Sum[b[tg-1, Append[p, e]], {e, mv}]]];
%t a[n_] := b[n]/2;
%t Table[an = a[n]; Print[an]; an, {n, 1, 16}] (* _Jean-François Alcover_, Nov 02 2018, after _Giovanni Resta_ in A001411 *)
%Y A001411 is the main entry for this sequence.
%Y Cf. A046661.
%K nonn,walk
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Hugo Pfoertner_, Dec 23 2002