A238831 a(n) = 0 if n <= 2; thereafter a(n) = A238827(n) + A238830(n-2).

0, 0, 0, 0, 0, 1, 3, 8, 21, 49, 124, 295, 735, 1789, 4428, 10874, 26836, 66062, 162838, 401081, 988225, 2434388, 5997403, 14774547, 36397880, 89667011, 220898267, 544190131, 1340632638, 3302695932, 8136311688, 20044096016, 49379354928, 121647818677, 299683787423, 738281805364, 1818783831517

Offset: 1

Author

N. J. A. Sloane, Mar 08 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• V. M. Zhuravlev, Horizontally-convex polyiamonds and their generating functions, Mat. Pros. 17 (2013), 107-129 (in Russian). See the sequence q(n).
• Index entries for linear recurrences with constant coefficients, signature (1,5,-1,-7,-1,6,6,1,-1).

Crossrefs

Cf. A238823-A238830.

Programs

Magma

m:=40; R:=LaurentSeriesRing(RationalField(), m); [0,0,0,0,0] cat Coefficients(R! -x^6*(x-1)*(2*x+1)*(x^2+x+1) / ((x+1)^2*(x^7-3*x^6-x^5-x^4+4*x^3-3*x+1))); // Vincenzo Librandi, Mar 21 2014

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

Mathematica

CoefficientList[Series[- x^5 (x - 1) (2 x + 1) (x^2 + x + 1)/((x + 1)^2 (x^7 - 3 x^6 - x^5 - x^4 + 4 x^3 - 3 x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 21 2014 *)

PARI

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