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

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: A292400 A007460 A034899 * A026153 A025180 A201967

Adjacent sequences: A026121 A026122 A026123 * A026125 A026126 A026127

Keyword

nonn

Author

Clark Kimberling

Status

approved