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

0, 0, 0, 1, 2, 6, 15, 36, 91, 218, 544, 1325, 3281, 8055, 19880, 48930, 120610, 297055, 731922, 1802994, 4441915, 10942602, 26957739, 66410994, 163606230, 403049273, 992926975, 2446110587, 6026082552, 14845470456, 36572353012, 90097307929

Offset

1,5

Links

Table of n, a(n) for n=1..32.

V. M. Zhuravlev, Horizontally-convex polyiamonds and their generating functions, Mat. Pros. 17 (2013), 107-129 (in Russian). See the sequence i(n).

Index entries for linear recurrences with constant coefficients, signature (1,5,-1,-7,-1,6,6,1,-1).

Formula

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

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

Mathematica

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 *)

Crossrefs

Cf. A238823-A238829.

Sequence in context: A084798 A215149 A017923 * A018018 A030009 A061261

Adjacent sequences: A238827 A238828 A238829 * A238831 A238832 A238833

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 08 2014

Status

approved