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a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3, s(n) = 4. Also a(n) = T(n,n-4), where T is the array defined in A024996.
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%I #8 Jun 23 2013 07:51:50

%S 1,3,12,40,133,427,1352,4224,13080,40216,122980,374452,1136226,

%T 3438150,10380048,31279728,94114125,282804759,848886180,2545759328,

%U 7628718845,22845628531,68377674280,204560102800,611720539235,1828673918721

%N a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3, s(n) = 4. Also a(n) = T(n,n-4), where T is the array defined in A024996.

%C First differences of A025182.

%F Conjecture: -(n-4)*(n+4)*a(n) +(4*n+7)*(n-4)*a(n-1) +(-2*n^2+23*n-12)*a(n-2) -(4*n+3)*(n-4)*a(n-3) +3*(n-4)*(n-5)*a(n-4)=0. - _R. J. Mathar_, Jun 22 2013

%K nonn

%O 4,2

%A _Clark Kimberling_