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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.
3
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
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
KEYWORD
nonn
STATUS
approved