A026328 - OEIS

A026328

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, s(0) = 2, s(n) = 5. Also a(n) = T(n,n-3), where T is the array in A026323.

%I #6 Jun 23 2013 11:38:01

%S 1,4,15,50,161,504,1553,4730,14289,42900,128193,381654,1132950,

%T 3355392,9918990,29278012,86316259,254227980,748200145,2200619806,

%U 6469372932,19011518480,55853259800,164055406320,481804384035,1414857108756,4154663090529

%N 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, s(0) = 2, s(n) = 5. Also a(n) = T(n,n-3), where T is the array in A026323.

%F Conjecture: -(n+9)*(n-3)*a(n) +(6*n^2+21*n-128)*a(n-1) +(-9*n^2-3*n+152)*a(n-2) -4*(n+4)*(n-1)*a(n-3) +12*(n-1)*(n-2)*a(n-4)=0. - _R. J. Mathar_, Jun 23 2013

%K nonn

%O 3,2

%A _Clark Kimberling_