Number of squares in all tilings of a 3 X n rectangle using integer-sided square tiles.

Terms

a(0) =0a(1) =3a(2) =12a(3) =34a(4) =98a(5) =256a(6) =654a(7) =1625a(8) =3964a(9) =9533a(10) =22662a(11) =53373a(12) =124728a(13) =289572a(14) =668514a(15) =1535869a(16) =3513614a(17) =8008090a(18) =18191184a(19) =41200568a(20) =93064834a(21) =209710139a(22) =471520566a(23) =1058065647a(24) =2369890254a(25) =5299215579a(26) =11830941840a(27) =26375563624a(28) =58722396932a(29) =130576680919