%I #14 Jul 23 2017 12:39:05

%S 0,0,0,1,4,19,70,261,914,3177,10816,36566,122552,408840,1358032,

%T 4497995,14862112,49019688,161449208,531152855,1745892452,5734722698,

%U 18826352472,61777432510,202648614072,664569581090,2178948104572,7143067052707,23413795288008

%N Column 3 of triangle in A059317 (the Pascal "Rhombus").

%H Alois P. Heinz, <a href="/A267192/b267192.txt">Table of n, a(n) for n = 0..1000</a>

%H José L. Ramírez, <a href="http://arxiv.org/abs/1511.04577">The Pascal Rhombus and the Generalized Grand Motzkin Paths</a>, arXiv:1511.04577 [math.CO], 2015.

%F Conjecture: +(n-2)*(n-3)*(n+3)*a(n) -n*(2*n-1)*(n-2)*a(n-1) -(n-1)*(5*n^2-10*n+18)*a(n-2) +n*(2*n-3)*(n-2)*a(n-3) +n*(n+1)*(n-5)*a(n-4)=0. - _R. J. Mathar_, Jul 23 2017

%p T:= proc(n, k) option remember; `if`(min(n, k)<0, 0,

%p `if`(k=0, 1, T(n-1, k)+T(n-1, k-1)+T(n-1, k-2)+T(n-2, k-2)))

%p end:

%p a:= n-> T(n, n-3):

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Jan 24 2016

%t T[n_, k_] := T[n, k] = If[Min[n, k]<0, 0, If[k == 0, 1, T[n-1, k] + T[n-1, k-1] + T[n-1, k-2] + T[n-2, k-2]]];

%t a[n_] := T[n, n-3];

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jun 23 2017, after _Alois P. Heinz_ *)

%Y Cf. A059317, A106050, A106053.

%K nonn

%O 0,5

%A _N. J. A. Sloane_, Jan 22 2016

%E More terms from _Alois P. Heinz_, Jan 24 2016