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A348454 Irregular triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n^2) is the number of ways to tile an n X n chessboard with rook-connected polyominoes of area k.

%I A348454 #23 Oct 27 2021 20:17:59
%S A348454 1,1,2,0,1,1,0,10,0,0,0,0,0,1,1,36,0,117,0,0,0,70,0,0,0,0,0,0,0,1,1,0,
%T A348454 0,0,4006,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6728,80092,178939,
%U A348454 0,451206,0,0,442791,0,0,264500,0,0,0,0,0,80518,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,158753814,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N A348454 Irregular triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n^2) is the number of ways to tile an n X n chessboard with rook-connected polyominoes of area k.
%C A348454 This is an essentially identical triangle to A348452, except that the data in each row has effectively been reversed. Rather than copying everything here, please refer to A348452 for further information.
%e A348454 Triangle begins:
%e A348454 1,
%e A348454 1, 2, 0, 1,
%e A348454 1, 0, 10, 0, 0, 0, 0, 0, 1,
%e A348454 1, 36, 0, 117, 0, 0, 0, 70, 0, 0, 0, 0, 0, 0, 0, 1,
%e A348454 1, 0, 0, 0, 4006, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e A348454 1, 6728, 80092, 178939, 0, 451206, 0, 0, 442791, 0, 0, 264500, 0, 0, 0, 0, 0, 80518, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e A348454 1, 0, 0, 0, 0, 0, 158753814, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e A348454 ...
%Y A348454 Cf. A348452, A348453, A348455, and A348456.
%K A348454 nonn,tabf
%O A348454 1,3
%A A348454 _N. J. A. Sloane_, Oct 27 2021
%E A348454 More than the usual number of terms are given, in order to show the first seven rows.