A361001 - OEIS

A361001

Triangle read by rows: T(n,k) is the number of tilings of an n X k rectangle by integer-sided rectangular pieces that cannot be rearranged to produce a different tiling of the rectangle (except rotations and reflections of the original tiling), 1 <= k <= n.

%I #7 Mar 02 2023 06:22:18

%S 1,2,4,3,7,9,4,11,18,23,4,14,22,34,41,6,23,42,72,108

%N Triangle read by rows: T(n,k) is the number of tilings of an n X k rectangle by integer-sided rectangular pieces that cannot be rearranged to produce a different tiling of the rectangle (except rotations and reflections of the original tiling), 1 <= k <= n.

%F T(n,1) = A361003(n) = A000005(n) + floor((n-1)/2). (The first term corresponds to cases where all pieces have the same size, the second to cases where there are two pieces of different sizes.)

%e Triangle begins:

%e n\k| 1 2 3 4 5 6

%e ---+-------------------

%e 1 | 1

%e 2 | 2 4

%e 3 | 3 7 9

%e 4 | 4 11 18 23

%e 5 | 4 14 22 34 41

%e 6 | 6 23 42 72 108 ?

%e The T(3,3) = 9 nonrearrangeable tilings of the 3 X 3 square are: