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a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 3, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-2), where T is the array in A026120.
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%I #6 Jun 23 2013 11:01:05

%S 1,2,7,20,59,170,489,1400,4002,11428,32626,93160,266136,760800,

%T 2176644,6232896,17864841,51253794,147188535,423098404,1217371023,

%U 3505992050,10106384621,29158627592,84200265555,243345531806,703858089717

%N a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 3, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-2), where T is the array in A026120.

%F G.f.: z^2(1-z)^2M^4, with M the g.f. of the Motzkin numbers (A001006).

%F Conjecture: (n+6)*a(n) +(-5*n-19)*a(n-1) +4*n*a(n-2) +8*(n+1)*a(n-3) +(-5*n+22)*a(n-4) +3*(-n+5)*a(n-5)=0. - _R. J. Mathar_, Jun 23 2013

%Y First differences of A026109.

%K nonn

%O 2,2

%A _Clark Kimberling_