cp's OEIS Frontend

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.

%I A026125 #6 Jun 23 2013 11:02:01
%S A026125 1,3,11,35,110,336,1013,3021,8945,26345,77297,226161,660387,1925535,
%T A026125 5608710,16325814,47500227,138168589,401865485,1168854085,3400065944,
%U A026125 9892187162,28787163584,83796367200,243997380575,710704813221,2070833535813
%N 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.
%F A026125 G.f.: z^3(1-z)^2M^5, with M the g.f. of the Motzkin numbers (A001006).
%F A026125 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
%Y A026125 First differences of A026110.
%K A026125 nonn
%O A026125 3,2
%A A026125 _Clark Kimberling_