A238828 a(0)=0; thereafter a(n) = A238824(n-1)+A238825(n).

0, 0, 1, 2, 5, 12, 28, 70, 169, 420, 1030, 2546, 6266, 15452, 38056, 93774, 230993, 569084, 1401913, 3453690, 8508214, 20960336, 51636447, 127208350, 313382262, 772028708, 1901920456, 4685449914, 11542774524, 28436041324, 70053211913, 172578611878

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..999 [Offset shifted by Georg Fischer, Oct 18 2021]

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

Index entries for linear recurrences with constant coefficients, signature (2,3,-4,-3,2,4,2,-1).

Formula

G.f.: x^2*(1-2*x^2+2*x^5) / ( (1+x)*(x^7-3*x^6-x^5-x^4+4*x^3-3*x+1) ). - R. J. Mathar, Mar 20 2014, adapted to offset Jun 19 2021

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
[seq(p(n+3)-p(n+1), 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
[0, seq(d(n-1)+p(n), n=2..32)]; #A238828

Mathematica

CoefficientList[Series[x^2 (1 - 2 x^2 + 2 x^5)/((1 + x) (x^7 - 3 x^6 - x^5 - x^4 + 4 x^3 - 3 x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 21 2014 *)
LinearRecurrence[{2, 3, -4, -3, 2, 4, 2, -1}, {0, 0, 1, 2, 5, 12, 28, 70}, 40] (* Harvey P. Dale, Aug 29 2023 *)

Prog

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

Crossrefs

Cf. A238823-A238827.

Sequence in context: A346051 A362893 A326760 * A326761 A162036 A321253

Adjacent sequences: A238825 A238826 A238827 * A238829 A238830 A238831

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 08 2014

Extensions

Offset corrected by N. J. A. Sloane, Jun 16 2021

Status

approved