A284231 Total number of nodes summed over all self-avoiding planar walks starting at (0,0), ending at (n,0), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1) with the restriction that (0,1) is never used below the diagonal and (1,0) is never used above the diagonal.

1, 5, 21, 152, 975, 8835, 75499, 830180, 8819417, 114384573, 1450018173, 21689509992, 319180726887, 5411092531323, 90615453774771, 1717272516535812, 32234085990345105, 675335923050095253, 14040521125141683717, 322252846702242056280, 7349647183279936080543

Offset: 0

Author

Alois P. Heinz, Mar 23 2017

Keywords

• nonn
• walk

Examples

			a(0) = 1: [(0,0)].
a(1) = 5: [(0,0),(1,0)], [(0,0),(0,1),(1,0)].
a(2) = 21: [(0,0),(1,0),(2,0)], [(0,0),(0,1),(1,0),(2,0)], [(0,0),(1,1),(2,0)], [(0,0),(0,1),(0,2),(1,1),(2,0)], [(0,0),(1,0),(0,1),(0,2),(1,1),(2,0)].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..446
• Wikipedia, Lattice path
• Wikipedia, Self-avoiding walk

Crossrefs

Cf. A277424, A284230, A284414, A285673.

Formula

a(n) = Sum_{k=n..n*(n+3)/2} (k+1) * A284414(n,k).