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A026031
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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.
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0
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1, 6, 28, 120, 494, 1988, 7888, 31008, 121125, 471086, 1826660, 7068360, 27313650, 105452700, 406923360, 1569869760, 6056194410, 23366193084, 90173331960, 348102883184, 1344324544156, 5193831553416, 20075820280544, 77637309982400
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OFFSET
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2,2
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LINKS
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FORMULA
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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
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
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MATHEMATICA
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Table[Binomial[2n, n-2]-Binomial[2n, n-6], {n, 2, 30}] (* Harvey P. Dale, May 28 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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