A026124 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.
1, 2, 7, 20, 59, 170, 489, 1400, 4002, 11428, 32626, 93160, 266136, 760800, 2176644, 6232896, 17864841, 51253794, 147188535, 423098404, 1217371023, 3505992050, 10106384621, 29158627592, 84200265555, 243345531806, 703858089717
Offset: 2
Keywords
Crossrefs
First differences of A026109.
Formula
G.f.: z^2(1-z)^2M^4, with M the g.f. of the Motzkin numbers (A001006).
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