A002900 Number of n-step walks on square lattice.

2, 6, 18, 50, 142, 390, 1086, 2958, 8134, 22050, 60146, 162466, 440750, 1187222, 3208298, 8622666, 23233338, 62329366, 167558310, 448848582, 1204403014, 3222280242, 8633306906, 23073198658, 61740677454, 164856393110, 440658745814

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• walk

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..79

Crossrefs

A001411 is the main entry for this sequence.

Cf. A046661.

Programs

Mathematica

(* 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}]]];
a[n_] := b[n]/2;
Table[an = a[n]; Print[an]; an, {n, 1, 16}] (* Jean-François Alcover, Nov 02 2018, after Giovanni Resta in A001411 *)

Formula

a(n) = (1/2) * A001411(n).

Extensions

More terms from Hugo Pfoertner, Dec 23 2002