A238826 a(n) = p(n+3)-p(n+1), where p(n) = A238825(n).

1, 2, 4, 9, 22, 53, 131, 323, 798, 1968, 4853, 11958, 29463, 72581, 178803, 440474, 1085110, 2673183, 6585468, 16223521, 39967243, 98460769, 242561730, 597559646, 1472109847, 3626595728, 8934249307, 22009844973, 54222045921, 133577963318, 329074124992, 810685962909

Offset

1,2

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 h(n).

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

Formula

G.f.: -x*(1+x)*(x^3+x^2-1)*(x-1)^2 / ( 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
[seq(p(n+3)-p(n+1), n=1..32)]; #A238826

Mathematica

CoefficientList[Series[-(1 + x) (x^3 + x^2 - 1) (x - 1)^2/(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); Coefficients(R! -x*(1+x)*(x^3+x^2-1)*(x-1)^2 / ( 1-3*x+4*x^3-x^4-x^5-3*x^6+x^7)); // Vincenzo Librandi, Mar 21 2014

Crossrefs

Cf. A238823-A238825.

Sequence in context: A369472 A055729 A317735 * A048211 A098719 A274289

Adjacent sequences: A238823 A238824 A238825 * A238827 A238828 A238829

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 08 2014

Status

approved