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Partial sums of A324964.
3

%I #14 Apr 24 2019 11:49:51

%S 0,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,

%T 6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,

%U 9,10,10,10,10,11,11,11

%N Partial sums of A324964.

%C Conjecture: a(n) <= A324918(n) for all n >= 13.

%H C. Defant, <a href="https://arxiv.org/abs/1903.09138">Counting 3-stack-sortable permutations</a>, arXiv:1903.09138 [math.CO], 2019.

%o (PARI) f(n) = binomial(3*n, n)*2/((n+1)*(2*n+1)) % 2; \\ A324964

%o a(n) = sum(k=0, n, f(k)); \\ _Michel Marcus_, Apr 02 2019

%Y Cf. A324964, A324965, A324918.

%K nonn

%O 0,6

%A _Colin Defant_, Mar 21 2019