A059512 For n>=2, the number of (s(0), s(1), ..., s(n-1)) such that 0 < s(i) < 5 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n-1, s(0) = 2, s(n-1) = 2.

0, 1, 1, 3, 7, 18, 46, 119, 309, 805, 2101, 5490, 14356, 37557, 98281, 257231, 673323, 1762594, 4614226, 12079707, 31624285, 82792161, 216750601, 567457058, 1485616392, 3889385353, 10182528721, 26658183099, 69791991919

Offset: 0

Author

Floor van Lamoen, Jan 21 2001

Keywords

• easy
• nonn

Comments

Substituting x(1-x)/(1-2x) into x/(1-x^2) yields g.f. of sequence.

Crossrefs

Cf. A000667, A059216, A059219, A059502, A027994.

a(1-2n)=A005207(2n), a(-2n)=A056014(2n+1).

Programs

Mathematica

CoefficientList[Series[x(1-x)(1-2x)/((1-x-x^2)(1-3x+x^2)), {x,0,30}], x]  (* Harvey P. Dale, Apr 23 2011 *)

PARI

a(n)=(fibonacci(2*n-1)+fibonacci(n-2))/2

Formula

a(n) = 2a(n-1) + Sum{mA000045).

G.f.: x(1-x)(1-2x)/((1-x-x^2)(1-3x+x^2)).

a(n+1)=sum{k=0..floor(n/2), C(n,2k)*F(2k+1)}. [From Paul Barry, Oct 14 2009]