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A284415 Number of self-avoiding planar walks of length n starting at (0,0), ending on the x-axis, 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. 3
1, 1, 3, 5, 14, 34, 96, 259, 748, 2142, 6329, 18727, 56358, 170370, 520354, 1596980, 4935307, 15319460, 47794472, 149681904, 470620062, 1484513696, 4697619876, 14906459690, 47426014833, 151247657528, 483426998881, 1548323383749, 4968516324954, 15972198595374 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..516

Alois P. Heinz, Animation of a(6)=96 walks

Wikipedia, Lattice path

Wikipedia, Self-avoiding walk

FORMULA

a(n) = Sum_{j=floor((sqrt(1+8*n)-1)/2)..n} A284414(j,n).

CROSSREFS

Column sums of A284414.

Cf. A001006, A003056.

Sequence in context: A271867 A295064 A052974 * A318227 A230585 A006395

Adjacent sequences:  A284412 A284413 A284414 * A284416 A284417 A284418

KEYWORD

nonn,walk

AUTHOR

Alois P. Heinz, Mar 26 2017

STATUS

approved

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Last modified August 11 09:47 EDT 2020. Contains 336423 sequences. (Running on oeis4.)