0,2

R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6

a(n) =sum_j[C(2n, 2j)c(j)c(j+1)c(n-j)] where c(k)=C(2k, k)/(k+1)=A000108(k)

a(1)=3 and a(2)=24 since if the possible steps are Right, Left, Up, Down, Forwards and Backwards, then the two-step paths are FB, RL and UD, while the four-step paths are FBFB, FBRL, FBUD, FFBB, FRBL, FRLB, FUBD, FUDB, RFBL, RFLB, RLFB, RLRL, RLUD, RRLL, RUDL, RULD, UDFB, UDRL, UDUD, UFBD, UFDB, URDL, URLD, UUDD.

Cf. A064036. The two- and one-dimensional equivalents are A005568 and A000108.

Sequence in context: A001099 A080523 A081133 this_sequence A128572 A052592 A059381

Adjacent sequences: A064034 A064035 A064036 this_sequence A064038 A064039 A064040

nonn

Henry Bottomley (se16(AT)btinternet.com), Aug 23 2001