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A238827 a(n) = 0 for n <= 3; thereafter a(n) = a(n-2)+A238825(n-3). 8
0, 0, 0, 0, 0, 0, 1, 2, 6, 13, 33, 77, 191, 464, 1147, 2819, 6956, 17132, 42228, 104026, 256303, 631394, 1555488, 3831945, 9440141, 23256017, 57292037, 141140858, 347705663, 856585345, 2110229136, 5198625560, 12807001916, 31550510748, 77725820617, 191480359254, 471718764310, 1162096170669 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

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 r(n).

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

FORMULA

G.f.: -x^7*(-1+x^2+x^3) / ( (1+x)*(x^7-3*x^6-x^5-x^4+4*x^3-3*x+1) ). - 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

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

MATHEMATICA

CoefficientList[Series[- x^6 (- 1 + x^2 + x^3)/((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 *)

PROG

(MAGMA) m:=40; R<x>:=LaurentSeriesRing(RationalField(), m); [0, 0, 0, 0, 0, 0] cat Coefficients(R! -x^7*(-1+x^2+x^3) / ( (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-A238826.

Sequence in context: A003039 A109385 A244578 * A098407 A151390 A116426

Adjacent sequences:  A238824 A238825 A238826 * A238828 A238829 A238830

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 08 2014

STATUS

approved

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Last modified October 17 22:05 EDT 2019. Contains 328134 sequences. (Running on oeis4.)