2,2

Number of (s(0), s(1), ..., s(n)) such that every s(i) is a nonnegative integer, s(0) = 0, s(1) = 1 = s(n), |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-1), where T is array in A026105, and U(n,n+1), where U is array in A026120.

Also number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 0, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2.

Number of Motzkin paths of length n+1 that start with a (1,1) step and end with a (1,-1) step. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 11 2001

The sequence 1,1,3,7,18.... has a(n)=sum{k=0..n, C(n,2k)*A000108(k+1) }. - Paul Barry (pbarry(AT)wit.ie), Jul 18 2003

a(n)=A001006(n+1)-2A001006(n)+A001006(n-1); g.f.: [(1-z)^2*M-1+z-z^2]/z, where M is the generating function of the Motzkin sequence A001006 (M = 1 + zM + z^2M^2).

Cf. A001006. First differences of A002026.

Cf. A026122.

Sequence in context: A052960 A059512 A094297 this_sequence A027969 A027971 A018028

Adjacent sequences: A026104 A026105 A026106 this_sequence A026108 A026109 A026110

nonn

Clark Kimberling (ck6(AT)evansville.edu)

Simpler definition from Ralf Stephan, Dec 16 2004