A235701 Number of n step walks (each step +/- 1 starting from 0) which are never more than 6 or less than -6.

1, 2, 4, 8, 16, 32, 64, 126, 252, 490, 980, 1890, 3780, 7252, 14504, 27734, 55468, 105840, 211680, 403368, 806736, 1535954, 3071908, 5845406, 11690812, 22238062, 44476124, 84582428, 169164856, 321661970, 643323940, 1223146232, 2446292464, 4650833040

Offset

0,2

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (0,7,0,-14,0,7)

Formula

G.f.: (1 + x - 2*x^2 - x^3)^2/(1 - 7*x^2 + 14*x^4 - 7*x^6).

Mathematica

nn=30; r=Solve[{s==1 + x a + x b, a==x s + x c, b==x s +x d, c==x a +x e, d==x b + x f, e==x c+x g, f==x d+x h, g==x e+x i, h==x f+x j, i==x g+x k, j==x h+x l, k==x i, l==x j, z==x k + x l }, {s, a, b, c, d, e, f, g, h, i, j, k, l, z}]; CoefficientList[Series[s+a+b+c+d+e+f+g+h+i+j+k+l/.r, {x, 0, nn}], x]

Crossrefs

Cf. A068911, A068912, A216212, A216241.

Row n=6 of A068913.

Sequence in context: A343844 A059174 A258585 * A054044 A325741 A008859

Adjacent sequences: A235698 A235699 A235700 * A235702 A235703 A235704

Keyword

nonn,walk,easy

Author

Geoffrey Critzer, Jan 14 2014

Status

approved