A061534 Expansion of (1-x^2)/(1-3*x-x^2+x^3).

1, 3, 9, 29, 93, 299, 961, 3089, 9929, 31915, 102585, 329741, 1059893, 3406835, 10950657, 35198913, 113140561, 363669939, 1168951465, 3757383773, 12077432845, 38820730843, 124782241601, 401090022801, 1289231579161, 4144002518683, 13320149112409

Offset

0,2

Comments

The number of tilings of a 2*n grid using dominoes and singletons with two horizontal dominoes or one vertical domino in the two rightmost squares. - John M. Campbell, Mar 05 2011

Links

Table of n, a(n) for n=0..26.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1056

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

Formula

a(n) = 3*a(n-1)+a(n-2)-a(n-3) for n>3. - Colin Barker, Sep 13 2014

G.f.: -(x-1)*(x+1) / (x^3-x^2-3*x+1). - Colin Barker, Sep 13 2014

a(n) = A033505(n)-A033505(n-2). - R. J. Mathar, Oct 24 2015

Prog

(PARI) Vec(-(x-1)*(x+1)/(x^3-x^2-3*x+1)  + O(x^100)) \\ Colin Barker, Sep 13 2014

Crossrefs

Cf. A033505.

Sequence in context: A098589 A024744 A024964 * A300044 A356937 A071728

Adjacent sequences: A061531 A061532 A061533 * A061535 A061536 A061537

Keyword

nonn,easy

Author

Henry Bottomley, May 16 2001

Status

approved