A238832 a(1)=0; thereafter a(n) = A238824(n-1)+A238830(n-1).

0, 0, 1, 1, 4, 9, 23, 58, 141, 353, 861, 2134, 5236, 12924, 31798, 78382, 193029, 475619, 1171600, 2886427, 7110657, 17517598, 43154977, 106314193, 261908415, 645221312, 1589525242, 3915853416, 9646844896, 23765351096, 58546797181, 144232146189, 355321086856, 875346302897, 2156447153427, 5312485264678

Offset: 1

Author

N. J. A. Sloane, Mar 08 2014

Keywords

• nonn
• easy

Links

• V. M. Zhuravlev, Horizontally-convex polyiamonds and their generating functions, Mat. Pros. 17 (2013), 107-129 (in Russian). See the sequence e(n).
• Index entries for linear recurrences with constant coefficients, signature (1,5,-1,-7,-1,6,6,1,-1).

Crossrefs

Cf. A238823-A238831.

Programs

Maple

g:=proc(n) option remember; local t1; t1:=[2,3,6,14,34,84,208,515];
if n <= 7 then t1[n] else
3*g(n-1)-4*g(n-3)+g(n-4)+g(n-5)+3*g(n-6)-g(n-7); fi; end proc;
[seq(g(n),n=1..32)]; # A238823
d:=proc(n) option remember; global g; local t1; t1:=[0,1];
if n <= 2 then t1[n] else
g(n-1)-2*d(n-1)-d(n-2); fi; end proc;
[seq(d(n),n=1..32)]; # A238824
p:=proc(n) option remember; global d; local t1; t1:=[0,0,0,1];
if n <= 4 then t1[n] else
p(n-2)+p(n-3)+2*(d(n-3)+d(n-4)); fi; end proc;
[seq(p(n),n=1..32)]; # A238825
h:=n->p(n+3)-p(n+1); [seq(h(n),n=1..32)]; #A238826
r:=proc(n) option remember; global p; local t1; t1:=[0,0,0,0];
if n <= 4 then t1[n] else
r(n-2)+p(n-3); fi; end proc;
[seq(r(n),n=1..32)]; # A238827
b:=n-> if n=1 then 0 else d(n-1)+p(n); fi; [seq(b(n),n=1..32)]; #A238828
a:=n->g(n)-h(n); [seq(a(n),n=1..32)]; #A238829
i:=proc(n) option remember; global b,r; local t1; t1:=[0,0];
if n <= 2 then t1[n] else
i(n-2)+b(n-1)+r(n); fi; end proc;
[seq(i(n),n=1..32)]; # A238830
q:=n-> if n<=2 then 0 else r(n)+i(n-2); fi;
[seq(q(n),n=1..45)]; # A238831
e:=n-> if n<=1 then 0 else d(n-1)+i(n-1); fi;
[seq(e(n),n=1..45)]; # A238832

PARI

concat([0,0], Vec(x^3*(2*x^5+2*x^4+x^3-2*x^2+1)/((x+1)^2*(x^7-3*x^6-x^5-x^4+4*x^3-3*x+1)) + O(x^100))) \\ Colin Barker, Mar 20 2014

Formula

G.f.: x^3*(2*x^5+2*x^4+x^3-2*x^2+1) / ((x+1)^2*(x^7-3*x^6-x^5-x^4+4*x^3-3*x+1)). - Colin Barker, Mar 20 2014