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%I #12 Jun 26 2022 23:17:47
%S 0,0,2,5,3,9,23,25,44,113,161,244,561,930,1405,2865,5137,8062,15082,
%T 27806,45582,81210,149637,254034,442904,806389,1400830,2428499,
%U 4362924,7674434,13329558,23699803,41904969,73097351,129121535,228531847
%N Number of tilings of 2 X n rectangle with polyominoes, each of which has area = # of adjacent polyominoes.
%F Complicated linear recurrence in terms of 4 variables known.
%F Empirical g.f.: -x^3*(2*x^8 + 4*x^5 + 4*x^4 + 3*x^3 + 3*x^2 + 5*x + 2) / (2*x^10 + 4*x^7 + 3*x^6 + x^5 + 2*x^4 + 3*x^3 - 1). [_Colin Barker_, Nov 29 2012]
%e a(5)=3 because of the tilings
%e aaabb aabbb abbbc
%e ccddd cccdd adddc
%K nonn
%O 1,3
%A I seem to have no record of the source for this sequence. - _N. J. A. Sloane_