%I #11 Mar 03 2024 12:40:22
%S 1,1,2,4,7,12,23,40,72,131,233,420,756,1355,2438,4381,7868,14144,
%T 25413,45661,82058,147444,264943,476092,855483,1537236,2762296,
%U 4963591,8919173,16027012,28799164,51749715,92989886,167094985,300255720
%N Antidiagonal sums of triangle A099602, in which row n equals the inverse binomial transform of column n of the triangle of trinomial coefficients (A027907).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2, 3, 0, -2, -1).
%F G.f.: (1+x-x^3)/(1-2*x^2-3*x^3+2*x^5+x^6).
%F a(n) = 2*a(n-2) + 3*a(n-3) - 2*a(n-5) - a(n-6) for n>=6.
%t LinearRecurrence[{0, 2, 3, 0, -2, -1}, {1, 1, 2, 4, 7, 12}, 35] (* _Jean-François Alcover_, Oct 30 2017 *)
%o (PARI) a(n)=polcoeff((1+x-x^3)/(1-2*x^2-3*x^3+2*x^5+x^6)+x*O(x^n),n,x)
%Y Cf. A099602, A027907.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 25 2004