A002900 Number of n-step walks on square lattice. (Formerly M1621 N0634)

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

1,1

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

Formula

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

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 *)

Crossrefs

A001411 is the main entry for this sequence.

Cf. A046661.

Sequence in context: A361286 A180282 A081154 * A309087 A199770 A204322

Adjacent sequences: A002897 A002898 A002899 * A002901 A002902 A002903

Keyword

nonn,walk

Author

N. J. A. Sloane

Extensions

More terms from Hugo Pfoertner, Dec 23 2002

Status

approved