OFFSET
1,2
LINKS
C. Defant, Poset Pattern-Avoidance Problems Posed by Yakoubov, arXiv:1608.03951 [math.CO], 2016.
S. Yakoubov, Pattern Avoidance in Extensions of Comb-Like Posets, arXiv preprint arXiv:1310.2979 [math.CO], 2013.
FORMULA
Define F_{2,3}(k)=1 if 2<=k<=4 and 0 otherwise. For s>=3, let F_{s,3}(k) = Sum_{i=(s-1)..(k-1)} (F_{s-1,3}(i)*Sum_{j=(k-3s+4)..2} (binomial(k-i-1,j))). Then a(n) = Sum_{k=n..(3n-2)} (binomial(3n-k,2)*F_{n,3}(k)). - Colin Defant, Aug 16 2016
MATHEMATICA
F[1, 3][1] = 1;
F[2, 3][k_] := If[2 <= k <= 4, 1, 0 ];
F[s_ /; s >= 3, 3][k_] := F[s, 3][k] = Sum[F[s - 1, 3][i] Sum[Binomial[k - i - 1, j], {j, k - 3s + 4, 2}], {i, s - 1, k - 1}];
a[n_] := Sum[Binomial[3n - k, 2] F[n, 3][k], {k, n, 3n - 2}];
Table[a[n], {n, 1, 19}] (* Jean-François Alcover, Jan 09 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 28 2013
EXTENSIONS
a(5)-a(9) from Colin Defant, Aug 16 2016
a(10)-a(19) from Alois P. Heinz, Aug 18 2016
STATUS
approved