A238825 a(1)..a(4) = 0,0,0,1; thereafter a(n) = a(n-2)+a(n-3)+2*(d(n-3)+d(n-4)) where d(n) = A238824(n).

0, 0, 0, 1, 2, 5, 11, 27, 64, 158, 387, 956, 2355, 5809, 14313, 35272, 86894, 214075, 527368, 1299185, 3200551, 7884653, 19424072, 47851896, 117884841, 290413626, 715444487, 1762523473, 4342040215, 10696772780, 26351885188, 64918818701

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 p(n).
• Index entries for linear recurrences with constant coefficients, signature (3,0,-4,1,1,3,-1).

Programs

Magma

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

Mathematica

CoefficientList[Series[x^3 (x - 1) (x^3 + x^2 - 1)/(1 - 3 x + 4 x^3 - x^4 - x^5 - 3 x^6 + x^7), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 21 2014 *)
LinearRecurrence[{3,0,-4,1,1,3,-1},{0,0,0,1,2,5,11,27},40] (* Harvey P. Dale, Aug 17 2025 *)

Formula

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