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A238831 a(n) = 0 if n <= 2; thereafter a(n) = A238827(n) + A238830(n-2). 5
0, 0, 0, 0, 0, 1, 3, 8, 21, 49, 124, 295, 735, 1789, 4428, 10874, 26836, 66062, 162838, 401081, 988225, 2434388, 5997403, 14774547, 36397880, 89667011, 220898267, 544190131, 1340632638, 3302695932, 8136311688, 20044096016, 49379354928, 121647818677, 299683787423, 738281805364, 1818783831517 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

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 q(n).

Index entries for linear recurrences with constant coefficients, signature (1,5,-1,-7,-1,6,6,1,-1).

FORMULA

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

h:=n->p(n+3)-p(n+1); [seq(h(n), 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

b:=n-> if n=1 then 0 else d(n-1)+p(n); fi; [seq(b(n), n=1..32)]; #A238828

a:=n->g(n)-h(n); [seq(a(n), n=1..32)]; #A238829

i:=proc(n) option remember; global b, r; local t1; t1:=[0, 0];

if n <= 2 then t1[n] else

i(n-2)+b(n-1)+r(n); fi; end proc;

[seq(i(n), n=1..32)]; # A238830

q:=n-> if n<=2 then 0 else r(n)+i(n-2); fi;

[seq(q(n), n=1..45)]; # A238831

MATHEMATICA

CoefficientList[Series[- x^5 (x - 1) (2 x + 1) (x^2 + x + 1)/((x + 1)^2 (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

(PARI) concat([0, 0, 0, 0, 0], Vec(-x^6*(x-1)*(2*x+1)*(x^2+x+1)/((x+1)^2*(x^7-3*x^6-x^5-x^4+4*x^3-3*x+1)) + O(x^100))) \\ Colin Barker, Mar 20 2014

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

CROSSREFS

Cf. A238823-A238830.

Sequence in context: A071078 A179903 A193045 * A322059 A259714 A096770

Adjacent sequences:  A238828 A238829 A238830 * A238832 A238833 A238834

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 08 2014

STATUS

approved

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Last modified August 24 02:32 EDT 2019. Contains 326260 sequences. (Running on oeis4.)