A162676
Number of different fixed (possibly) disconnected n-ominoes bounded (not necessarily tightly) by an n*n square.
Original entry on oeis.org
1, 4, 48, 956, 26490, 937342, 40291608, 2036155284, 118202408622, 7747410899954, 565695467415936, 45525704815717568, 4002930269944724664, 381750656962687053108, 39244733577786624617904, 4325973539461955182836900, 508971415418900757219557142
Offset: 1
a(2)=4: the two rotations of the (connected) domino and the two rotations of the disconnected domino consisting of two squares connected at a vertex.
-
Table[Binomial[n^2,n]-2*Binomial[(n-1)n,n]+Binomial[(n-1)^2,n],{n,20}] (* Harvey P. Dale, Oct 01 2013 *)
-
a(n) = binomial(n^2,n) - 2*binomial((n-1)*n,n) + binomial((n-1)^2,n); \\ Michel Marcus, Aug 30 2013
A162674
Number of different fixed (possibly) disconnected tetrominoes bounded (not necessarily tightly) by an n X n square.
Original entry on oeis.org
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
a(2)=1: the (connected) square tetromino.
A162677
Number of different fixed (possibly) disconnected polyominoes (of any area) bounded (not necessarily tightly) by an n*n square.
Original entry on oeis.org
1, 10, 400, 57856, 31522816, 66605547520, 554222579875840, 18303191835587117056, 2408425353007592768536576, 1265177138001297870205254369280, 2655861110791164560222750369099284480
Offset: 1
a(2)=10: the monomino, 4 dominoes (2 strictly disconnected), 4 rotations of the L tromino, and the square tetromino.
A163435
Number of different fixed (possibly) disconnected pentominoes bounded tightly by an n X n square.
Original entry on oeis.org
0, 0, 102, 1792, 11550, 46848, 144550, 371712, 838782, 1715200, 3247398, 5779200, 9774622, 15843072, 24766950, 37531648, 55357950, 79736832, 112466662, 155692800, 211949598, 284204800, 375906342, 491031552, 634138750, 810421248
Offset: 1
a(3) = 102: there are 102 rotations of the 19 free (possibly) disconnected pentominoes bounded tightly by a 3 X 3 square; these include the F, T, V, W, X and Z (connected) pentominoes and 13 strictly disconnected free pentominoes.
-
Join[{0}, Table[(2/3)*n^2*(n - 2)^2*(5*n^2 - 10*n + 2), {n, 2, 50}]] (* or *) Join[{0}, LinearRecurrence[{7,-21,35,-35,21,-7,1}, {0, 102, 1792, 11550, 46848, 144550, 371712}, 50]] (* G. C. Greubel, Dec 23 2016 *)
-
concat([0,0], Vec(2*x^3*(51+539*x+574*x^2+30*x^3+7*x^4-x^5)/ (1-x)^7 + O(x^50))) \\ G. C. Greubel, Dec 23 2016
Showing 1-4 of 4 results.
Comments