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%I #14 May 18 2022 17:40:39
%S 1,1,0,1,1,3,1,0,7,8,1,1,17,81,702,1,0,41,184,4623,41952,1,1,99,1051,
%T 35044,654673,16600824,1,0,239,3176,248045,7407376,358635313,
%U 13298557992,1,1,577,14609,1819731,100694199,8448412164,569631442289,43157780553934
%N Triangle read by rows: T(k,n) (k >= 0, n = 0, ..., k) = number of tilings of a k X n rectangle using 2 X 2 tiles, right trominoes and dominoes.
%C For tiling algorithm, see A351322.
%C Reading the sequence {T(k,n)}, use T(n,k) instead of T(k,n) for n>k.
%C T(1,n) = A000035(n+1) = (n+1) mod 2,
%C T(2,n) = A001333(n), T(3,n) = A354011(n), T(4,n) = A354012(n).
%e Triangle begins
%e k\n 0 1 2 3 4 5 6
%e -----------------------------------------
%e 0 1
%e 1 1 0
%e 2 1 1 3
%e 3 1 0 7 8
%e 4 1 1 17 81 702
%e 5 1 0 41 184 4623 41952
%e 6 1 1 99 1051 35044 654673 16600824
%o (Maxima) See A352589.
%Y Cf. A000035, A001333, A351322, A352589, A354011, A354012.
%Y T(n,n) gives A354119.
%K nonn,tabl
%O 0,6
%A _Gerhard Kirchner_, May 14 2022