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A052908 Expansion of 1 + x/(1 - 2*x - x^3 + x^4). 1
1, 1, 2, 4, 9, 19, 40, 85, 180, 381, 807, 1709, 3619, 7664, 16230, 34370, 72785, 154136, 326412, 691239, 1463829, 3099934, 6564695, 13901980, 29440065, 62344891, 132027067, 279592219, 592089264, 1253860704, 2655286560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Let A(r,n) count the total number of ordered arrangements of an n+r tiling of r red squares and white tiles of total length n, where the individual tile lengths can range from 1 to n. A(r,0) corresponds to a tiling of r red squares only. Let A_1(r,n) = Sum_{j=0..n} A(r,j). Then the expansion of 1/(1-2*x-x^3+x^4) = A_1(0,n) + A_1(1,n-3) + A_1(2, n-6) + ..., which generates a(n) without the initial 1. - Gregory L. Simay, May 24 2018

LINKS

Table of n, a(n) for n=0..30.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 888

Index entries for linear recurrences with constant coefficients, signature (2,0,1,-1).

FORMULA

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

Recurrence: {a(1)=1, a(0)=1, a(3)=4, a(2)=2, a(4)=9, a(n) - a(n+1) - 2*a(n+3) + a(n+4) = 0}.

Sum(-1/643*(74*_alpha-53*_alpha^2+93*_alpha^3-168)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-_Z^3+_Z^4)).

MAPLE

spec := [S, {S=Sequence(Prod(Sequence(Z), Sequence(Prod(Z, Z, Z)), Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

MATHEMATICA

CoefficientList[Series[(-1 + x) (-1 + x^3)/(1 - 2 x - x^3 + x^4), {x, 0, 30}], x] (* Michael De Vlieger, Jun 14 2018 *)

CROSSREFS

Sequence in context: A011955 A084172 A018100 * A036616 A136298 A122584

Adjacent sequences:  A052905 A052906 A052907 * A052909 A052910 A052911

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

More terms from James A. Sellers, Jun 05 2000

STATUS

approved

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Last modified September 19 12:57 EDT 2019. Contains 327198 sequences. (Running on oeis4.)