A212585 Walks of length n on the x-axis using steps {1,-1} and visiting no point more than twice.

1, 2, 4, 8, 12, 18, 26, 40, 56, 82, 112, 162, 222, 316, 432, 608, 834, 1166, 1602, 2228, 3066, 4252, 5858, 8108, 11178, 15454, 21316, 29450, 40632, 56114, 77434, 106914, 147550, 203696, 281134, 388082, 535636, 739368, 1020506, 1408626, 1944266, 2683674, 3704184

Offset

0,2

Links

Table of n, a(n) for n=0..42.

Formula

G.f. (-1-x-2*x^3+3*x^5-2*x^7+x^8)/((-1+x^2)^2 * (-1+x+x^4)).

a(0)=1; a(n) = 2*(A212584(n) + sum(j,1-mod(n,2) .. n-3, step+2, A212584(j))).

Mathematica

CoefficientList[Series[(-1-x-2*x^3+3*x^5-2*x^7+x^8)/((-1+x^2)^2 * (-1+x+x^4)), {x, 0, 45}], x]

Crossrefs

Cf. A212584, A212586, A212587, A164392, A212589.

Sequence in context: A053799 A343949 A284122 * A085891 A006501 A224814

Adjacent sequences: A212582 A212583 A212584 * A212586 A212587 A212588

Keyword

nonn,walk

Author

David Scambler, May 22 2012

Status

approved