cp's OEIS Frontend

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.

%I A026123 #8 Jul 08 2022 10:53:10
%S A026123 1,4,10,28,76,209,575,1589,4405,12253,34189,95679,268503,755457,
%T A026123 2130717,6023235,17063139,48434514,137741280,392407134,1119766942,
%U A026123 3200326627,9160055809,26254474379,75348899051,216515177336,622887159274
%N 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.
%F A026123 G.f.: z^2(-1+(1-z)^2M^3), with M the g.f. of the Motzkin numbers (A001006).
%F A026123 D-finite with recurrence: (n+5)*a(n) +5*(-n-3)*a(n-1) +(5*n+1)*a(n-2) +(5*n+3)*a(n-3) +6*(-n+3)*a(n-4)=0. - _R. J. Mathar_, Jun 23 2013
%Y A026123 First differences of A026134.
%K A026123 nonn
%O A026123 2,2
%A A026123 _Clark Kimberling_