cp's OEIS Frontend

A026109 a(n) = 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) = 3, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-3), where T is the array defined in A026105.

%I A026109 #6 Jun 23 2013 10:45:02
%S A026109 1,3,10,30,89,259,748,2148,6150,17578,50204,143364,409500,1170300,
%T A026109 3346944,9579840,27444681,78698475,225887010,648985414,1866356437,
%U A026109 5372348487,15478733108,44637360700,128837626255,372183158061,1076041247778
%N A026109 a(n) = 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) = 3, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-3), where T is the array defined in A026105.
%F A026109 G.f.: z(1-z)M^4, with M the g.f. of the Motzkin numbers (A001006).
%F A026109 Conjecture: (n+5)*a(n) +5*(-n-3)*a(n-1) +4*n*a(n-2) +8*n*a(n-3) +(-5*n+19)*a(n-4) +3*(-n+5)*a(n-5)=0. - _R. J. Mathar_, Jun 23 2013
%Y A026109 First differences of A005323. Cf. A026124.
%K A026109 nonn
%O A026109 3,2
%A A026109 _Clark Kimberling_