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a(n) = number of (s(0), s(1), ..., s(2n-1)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 2, s(2n-1) = 7. Also a(n) = T(2n-1,n-3), where T is the array defined in A026009.
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%I #6 Jun 20 2013 16:26:58

%S 1,7,36,164,702,2898,11696,46512,183141,716243,2788060,10817820,

%T 41880930,161900910,625272480,2413491360,9313307370,35936613414,

%U 138680365704,535290282632,2066802226236,7983111461732,30848211650592

%N a(n) = number of (s(0), s(1), ..., s(2n-1)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 2, s(2n-1) = 7. Also a(n) = T(2n-1,n-3), where T is the array defined in A026009.

%F Conjecture: -(n+5)*(3*n-37)*a(n) +3*(-n^2-84*n-173)*a(n-1) +2*(32*n^2+295*n+254)*a(n-2) -8*(n+25)*(2*n-5)*a(n-3)=0. - _R. J. Mathar_, Jun 20 2013

%Y First differences if A003518.

%K nonn

%O 3,2

%A _Clark Kimberling_