Voozh

A026124

a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 3, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-2), where T is the array in A026120.

1, 2, 7, 20, 59, 170, 489, 1400, 4002, 11428, 32626, 93160, 266136, 760800, 2176644, 6232896, 17864841, 51253794, 147188535, 423098404, 1217371023, 3505992050, 10106384621, 29158627592, 84200265555, 243345531806, 703858089717

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OFFSET

2,2

LINKS

Table of n, a(n) for n=2..28.

FORMULA

G.f.: z^2(1-z)^2M^4, with M the g.f. of the Motzkin numbers (A001006).

Conjecture: (n+6)*a(n) +(-5*n-19)*a(n-1) +4*n*a(n-2) +8*(n+1)*a(n-3) +(-5*n+22)*a(n-4) +3*(-n+5)*a(n-5)=0. - R. J. Mathar, Jun 23 2013

CROSSREFS

First differences of A026109.

Sequence in context: A389120 A007460 A034899 * A026153 A025180 A201967

Adjacent sequences: A026121 A026122 A026123 * A026125 A026126 A026127