A026125 a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 4, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-3), where T is the array in A026120.
1, 3, 11, 35, 110, 336, 1013, 3021, 8945, 26345, 77297, 226161, 660387, 1925535, 5608710, 16325814, 47500227, 138168589, 401865485, 1168854085, 3400065944, 9892187162, 28787163584, 83796367200, 243997380575, 710704813221, 2070833535813
Offset: 3
Keywords
Crossrefs
First differences of A026110.
Formula
G.f.: z^3(1-z)^2M^5, with M the g.f. of the Motzkin numbers (A001006).
Conjecture: -(n+7)*(n-3)*a(n) +(4*n+17)*(n-3)*a(n-1) +(-2*n^2+13*n+27)*a(n-2) -(4*n+5)*(n-3)*a(n-3) +3*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Jun 23 2013