A026109 a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is a nonnegative integer, s(0) = 0, s(1) = 1, s(n) = 3, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-3), where T is the array defined in A026105.

1, 3, 10, 30, 89, 259, 748, 2148, 6150, 17578, 50204, 143364, 409500, 1170300, 3346944, 9579840, 27444681, 78698475, 225887010, 648985414, 1866356437, 5372348487, 15478733108, 44637360700, 128837626255, 372183158061, 1076041247778

Offset

3,2

Links

Table of n, a(n) for n=3..29.

Formula

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

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

Crossrefs

First differences of A005323. Cf. A026124.

Sequence in context: A094306 A257596 A261336 * A026327 A014531 A062107

Adjacent sequences: A026106 A026107 A026108 * A026110 A026111 A026112

Keyword

nonn

Author

Clark Kimberling

Status

approved