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A026123
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a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 2, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-1), where T is the array in A026120; a(n) = U(n,n+1), where U is the array in A026148.
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3
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1, 4, 10, 28, 76, 209, 575, 1589, 4405, 12253, 34189, 95679, 268503, 755457, 2130717, 6023235, 17063139, 48434514, 137741280, 392407134, 1119766942, 3200326627, 9160055809, 26254474379, 75348899051, 216515177336, 622887159274
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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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G.f.: z^2(-1+(1-z)^2M^3), with M the g.f. of the Motzkin numbers (A001006).
D-finite with recurrence: (n+5)*a(n) +5*(-n-3)*a(n-1) +(5*n+1)*a(n-2) +(5*n+3)*a(n-3) +6*(-n+3)*a(n-4)=0. - R. J. Mathar, Jun 23 2013
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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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