A173963 Number of nonoverlapping placements of one 1 X 1 square and one 2 X 2 square on an n X n board.

0, 0, 20, 108, 336, 800, 1620, 2940, 4928, 7776, 11700, 16940, 23760, 32448, 43316, 56700, 72960, 92480, 115668, 142956, 174800, 211680, 254100, 302588, 357696, 420000, 490100, 568620, 656208, 753536, 861300, 980220, 1111040, 1254528

Offset

1,3

Comments

Also the number of placements of a horizontal and a vertical domino on the n X n board. - Ralf Stephan, Jun 10 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (n^2 - 4) * (n-1)^2.

a(n) = A000290(n-1)*A028347(n) = A085740(n-1)/4;

a(n) = A002378(n-2)*A028552(n-1), for n > 1.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), with a(1)=0, a(2)=0, a(3)=20, a(4)=108, a(5)=336. - Harvey P. Dale, Aug 16 2011

G.f.: (4*x^3*((x-2)*x-5))/(x-1)^5. - Harvey P. Dale, Aug 16 2011

Mathematica

Table[(n^2-4)(n-1)^2, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 20, 108, 336}, 40] (* Harvey P. Dale, Aug 16 2011 *)

Prog

(Magma) [(n^2 - 4) * (n-1)^2: n in [1..40]]; // Vincenzo Librandi, Sep 14 2011

Crossrefs

Sequence in context: A209547 A278642 A135174 * A202957 A232586 A189437

Adjacent sequences: A173960 A173961 A173962 * A173964 A173965 A173966

Keyword

nonn,easy

Author

Reinhard Zumkeller, Mar 03 2010

Status

approved