%I A026023
%S A026023 1,2,4,8,15,30,56,112,210,420,792,1584,3003,6006,11440,22880,43758,87516,
%T A026023 167960,335920,646646,1293292,2496144,4992288,9657700,19315400,37442160,
%U A026023 74884320,145422675,290845350,565722720,1131445440,2203961430,4407922860
%N A026023 a(n) = number of (s(0), s(1), ..., s(n)) such that s(i) is a nonnegative 
               integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n and s(0) = 3. Also 
               a(n) = Sum{T(n,k), k = 0,1,...,[ (n+3)/2 ]}, where T is defined in 
               A026022.
%F A026023 a(2n) = C(2n+2, n), a(2n+1) = 2a(2n).
%F A026023 E.g.f.: dif(Bessel_I(1,2x)+2*Bessel_I(2,2x)+Bessel_I(3,2x),x); - Paul 
               Barry (pbarry(AT)wit.ie), Jun 09 2007
%F A026023 O.g.f.:-1/2*(-1+4*x^2+(1-8*x^2+20*x^4-16*x^6)^(1/2))/x^4/(2*x-1) [From 
               Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
%Y A026023 Sequence in context: A000078 A034338 A166861 this_sequence A077596 A091865 
               A065494
%Y A026023 Adjacent sequences: A026020 A026021 A026022 this_sequence A026024 A026025 
               A026026
%K A026023 nonn
%O A026023 0,2
%A A026023 Clark Kimberling (ck6(AT)evansville.edu)
%E A026023 Definition corrected by Herbert Kociemba (kociemba(AT)t-online.de), May 
               08 2004