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A238830 a(1)=a(2)=0; thereafter a(n) = a(n-2)+A238828(n-1)+A238827(n).

%I A238830 #10 Dec 29 2021 15:30:03
%S A238830 0,0,0,1,2,6,15,36,91,218,544,1325,3281,8055,19880,48930,120610,
%T A238830 297055,731922,1802994,4441915,10942602,26957739,66410994,163606230,
%U A238830 403049273,992926975,2446110587,6026082552,14845470456,36572353012,90097307929
%N A238830 a(1)=a(2)=0; thereafter a(n) = a(n-2)+A238828(n-1)+A238827(n).
%H A238830 V. M. Zhuravlev, <a href="http://www.mccme.ru/free-books/matpros/mph.pdf">Horizontally-convex polyiamonds and their generating functions</a>, Mat. Pros. 17 (2013), 107-129 (in Russian). See the sequence i(n).
%H A238830 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-1,-7,-1,6,6,1,-1).
%F A238830 G.f.: x^4*(1+x-x^2+x^5) / ( (x^7-3*x^6-x^5-x^4+4*x^3-3*x+1)*(1+x)^2 ). - _R. J. Mathar_, Mar 20 2014
%p A238830 g:=proc(n) option remember; local t1; t1:=[2,3,6,14,34,84,208,515];
%p A238830 if n <= 7 then t1[n] else
%p A238830 3*g(n-1)-4*g(n-3)+g(n-4)+g(n-5)+3*g(n-6)-g(n-7); fi; end proc;
%p A238830 [seq(g(n),n=1..32)]; # A238823
%p A238830 d:=proc(n) option remember; global g; local t1; t1:=[0,1];
%p A238830 if n <= 2 then t1[n] else
%p A238830 g(n-1)-2*d(n-1)-d(n-2); fi; end proc;
%p A238830 [seq(d(n),n=1..32)]; # A238824
%p A238830 p:=proc(n) option remember; global d; local t1; t1:=[0,0,0,1];
%p A238830 if n <= 4 then t1[n] else
%p A238830 p(n-2)+p(n-3)+2*(d(n-3)+d(n-4)); fi; end proc;
%p A238830 [seq(p(n),n=1..32)]; # A238825
%p A238830 h:=n->p(n+3)-p(n+1); [seq(h(n),n=1..32)]; #A238826
%p A238830 r:=proc(n) option remember; global p; local t1; t1:=[0,0,0,0];
%p A238830 if n <= 4 then t1[n] else
%p A238830 r(n-2)+p(n-3); fi; end proc;
%p A238830 [seq(r(n),n=1..32)]; # A238827
%p A238830 b:=n-> if n=1 then 0 else d(n-1)+p(n); fi; [seq(b(n),n=1..32)]; #A238828
%p A238830 a:=n->g(n)-h(n); [seq(a(n),n=1..32)]; #A238829
%p A238830 i:=proc(n) option remember; global b,r; local t1; t1:=[0,0];
%p A238830 if n <= 2 then t1[n] else
%p A238830 i(n-2)+b(n-1)+r(n); fi; end proc;
%p A238830 [seq(i(n),n=1..32)]; # A238830
%t A238830 LinearRecurrence[{1,5,-1,-7,-1,6,6,1,-1},{0,0,0,1,2,6,15,36,91},40] (* _Harvey P. Dale_, Dec 29 2021 *)
%Y A238830 Cf. A238823-A238829.
%K A238830 nonn,easy
%O A238830 1,5
%A A238830 _N. J. A. Sloane_, Mar 08 2014