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A026125
a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 4, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-3), where T is the array in A026120.
3
1, 3, 11, 35, 110, 336, 1013, 3021, 8945, 26345, 77297, 226161, 660387, 1925535, 5608710, 16325814, 47500227, 138168589, 401865485, 1168854085, 3400065944, 9892187162, 28787163584, 83796367200, 243997380575, 710704813221, 2070833535813
OFFSET
3,2
FORMULA
G.f.: z^3(1-z)^2M^5, with M the g.f. of the Motzkin numbers (A001006).
Conjecture: -(n+7)*(n-3)*a(n) +(4*n+17)*(n-3)*a(n-1) +(-2*n^2+13*n+27)*a(n-2) -(4*n+5)*(n-3)*a(n-3) +3*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Jun 23 2013
CROSSREFS
First differences of A026110.
Sequence in context: A126939 A370199 A126940 * A026154 A025181 A004054
KEYWORD
nonn
STATUS
approved