A026123 a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 2, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-1), where T is the array in A026120; a(n) = U(n,n+1), where U is the array in A026148.

1, 4, 10, 28, 76, 209, 575, 1589, 4405, 12253, 34189, 95679, 268503, 755457, 2130717, 6023235, 17063139, 48434514, 137741280, 392407134, 1119766942, 3200326627, 9160055809, 26254474379, 75348899051, 216515177336, 622887159274