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

1,5

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).

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

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 *)

Prog

(Magma) m:=40; R<x>:=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

Crossrefs

Sequence in context: A095975 A006652 A340314 * A073225 A027087 A363579

Adjacent sequences: A238822 A238823 A238824 * A238826 A238827 A238828

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 08 2014

Status

approved