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A238829 a(n) = A238823(n) - A238826(n). 6
1, 1, 2, 5, 12, 31, 77, 192, 474, 1170, 2881, 7097, 17477, 43050, 106043, 261235, 643552, 1585421, 3905750, 9621993, 23704161, 58396118, 143860974, 354406732, 873093707, 2150897733, 5298813853, 13053818630, 32158552201, 79223751853, 195170567014, 480809724213 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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 a(n).

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

FORMULA

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

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

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

a:=n->g(n)-h(n);

[seq(a(n), n=1..32)]; #A238829

MATHEMATICA

CoefficientList[Series[(1 - x) (2 x^5 + x^4 + x^3 - 2 x^2 - x + 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 *)

LinearRecurrence[{3, 0, -4, 1, 1, 3, -1}, {1, 1, 2, 5, 12, 31, 77}, 40] (* Harvey P. Dale, Jun 08 2018 *)

PROG

(MAGMA) I:=[1, 1, 2, 5, 12, 31, 77]; [n le 7 select I[n] else 3*Self(n-1)-4*Self(n-3)+Self(n-4)+Self(n-5)+3*Self(n-6)-Self(n-7): n in [1..35]]

CROSSREFS

Cf. A238823-A238828.

Sequence in context: A305311 A291239 A193284 * A125023 A129804 A317882

Adjacent sequences:  A238826 A238827 A238828 * A238830 A238831 A238832

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 08 2014

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)