A284231 - OEIS

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

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OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..446

Wikipedia, Lattice path

Wikipedia, Self-avoiding walk

FORMULA

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

EXAMPLE

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)].

CROSSREFS

Cf. A277424, A284230, A284414, A285673.

Sequence in context: A228113 A306589 A221513 * A182825 A318966 A117067

Adjacent sequences: A284228 A284229 A284230 * A284232 A284233 A284234

KEYWORD

nonn,walk

AUTHOR

Alois P. Heinz, Mar 23 2017

STATUS

approved