A059512 - OEIS

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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

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OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..28.

FORMULA

a(n) = 2a(n-1) + Sum{m<n-1}a(m) - F(n-3) where F(n) is the n-th Fibonacci number (A000045).

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]

MATHEMATICA