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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. 6
1, 5, 21, 152, 975, 8835, 75499, 830180, 8819417, 114384573, 1450018173, 21689509992, 319180726887, 5411092531323, 90615453774771, 1717272516535812, 32234085990345105, 675335923050095253, 14040521125141683717, 322252846702242056280, 7349647183279936080543 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 13:55 EST 2020. Contains 331113 sequences. (Running on oeis4.)