A162674 Number of different fixed (possibly) disconnected tetrominoes bounded (not necessarily tightly) by an n X n square.

0, 1, 97, 956, 4780, 16745, 46921, 112672, 241536, 474585, 870265, 1508716, 2496572, 3972241, 6111665, 9134560, 13311136, 18969297, 26502321, 36377020, 49142380, 65438681, 86007097, 111699776, 143490400, 182485225, 229934601

Offset

1,3

Comments

Fixed quasi-tetrominoes.

Links

Table of n, a(n) for n=1..27.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = n*(n-1)*(8*n^4-16*n^3-9*n^2+17*n+8)/12.

G.f.: x^2*(1+90*x+298*x^2+90*x^3+x^4)/(1-x)^7. [Colin Barker, Apr 25 2012]

Example

a(2)=1: the (connected) square tetromino.

Crossrefs

Cf. A162673, A162675, A162676, A162677, A094171 (free quasi-tetrominoes).

Sequence in context: A045715 A113891 A090157 * A070845 A262925 A093297

Adjacent sequences: A162671 A162672 A162673 * A162675 A162676 A162677

Keyword

nonn,easy

Author

David Bevan, Jul 27 2009

Status

approved