A027053 a(n) = T(n,n+2), T given by A027052.

1, 4, 9, 18, 35, 66, 123, 228, 421, 776, 1429, 2630, 4839, 8902, 16375, 30120, 55401, 101900, 187425, 344730, 634059, 1166218, 2145011, 3945292, 7256525, 13346832, 24548653, 45152014, 83047503, 152748174, 280947695, 516743376

Offset

2,2

Comments

Second differences of (A027026(n)-1)/2.

Pairwise sums of A089068.

a(n) is also the number of fixed polyominoes with n cells of height (or width) 2. - David Bevan, Sep 09 2009

Links

G. C. Greubel, Table of n, a(n) for n = 2..1001

Doron Zeilberger, The generating functions and series expansions for 2D lattice-animals of globally bounded width. [Local copies of generating functions and series expansions].

Index entries for sequences related to polyominoes

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

Formula

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

a(n) = A089068(n-1) + A089068(n).

a(n) = a(n-1) + a(n-2) + a(n-3) + 4. - David Bevan, Sep 09 2009

a(n) = A001590(n+3) - 2. - David Bevan, Sep 09 2009

a(n+1) - a(n) = A000213(n+1). - R. J. Mathar, Aug 04 2013

Maple

seq(coeff(series(x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3)), x, n+1), x, n), n = 2 ..30); # G. C. Greubel, Nov 05 2019

Mathematica

LinearRecurrence[{2, 0, 0, -1}, {1, 4, 9, 18}, 30] (* G. C. Greubel, Nov 05 2019 *)

Prog

(PARI) my(x='x+O('x^32)); Vec(x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3))) \\ G. C. Greubel, Nov 05 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 32); Coefficients(R!( x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3)) )); // G. C. Greubel, Nov 05 2019
(Sage)
def A027053_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3))).list()
a=A027053_list(32); a[2:] # G. C. Greubel, Nov 05 2019
(GAP) a:=[1, 4, 9, 18];; for n in [5..30] do a[n]:=2*a[n-1]-a[n-4]; od; a; # G. C. Greubel, Nov 05 2019

Crossrefs

2nd column of A308359.

Sequence in context: A301150 A301078 A320851 * A122039 A083706 A352667

Adjacent sequences: A027050 A027051 A027052 * A027054 A027055 A027056

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved