cp's OEIS Frontend

A026031 a(n) = number of (s(0), s(1), ..., s(2n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 3, s(2n) = 7. Also a(n) = T(2n,n-2), where T is defined in A026022.

%I A026031 #11 May 28 2017 09:36:43
%S A026031 1,6,28,120,494,1988,7888,31008,121125,471086,1826660,7068360,
%T A026031 27313650,105452700,406923360,1569869760,6056194410,23366193084,
%U A026031 90173331960,348102883184,1344324544156,5193831553416,20075820280544,77637309982400
%N A026031 a(n) = number of (s(0), s(1), ..., s(2n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 3, s(2n) = 7. Also a(n) = T(2n,n-2), where T is defined in A026022.
%F A026031 C(2n, n-2) - C(2n, n-6). G.f.: (1+x^2C^4)*C^6, where C=(1-sqrt(1-4x))/(2x). - _Ralf Stephan_, Jan 09 2005
%F A026031 Conjecture: (n+6)*a(n) +10*(-n-4)*a(n-1) +2*(17*n+32)*a(n-2) +4*(-11*n+4)*a(n-3) +8*(2*n-5)*a(n-4)=0. - _R. J. Mathar_, Jun 22 2013
%t A026031 Table[Binomial[2n,n-2]-Binomial[2n,n-6],{n,2,30}] (* _Harvey P. Dale_, May 28 2017 *)
%K A026031 nonn
%O A026031 2,2
%A A026031 _Clark Kimberling_