Number of length-4 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

Terms

a(0) =11a(1) =67a(2) =229a(3) =581a(4) =1231a(5) =2311a(6) =3977a(7) =6409a(8) =9811a(9) =14411a(10) =20461a(11) =28237a(12) =38039a(13) =50191a(14) =65041a(15) =82961a(16) =104347a(17) =129619a(18) =159221a(19) =193621a(20) =233311a(21) =278807a(22) =330649a(23) =389401a(24) =455651a(25) =530011a(26) =613117a(27) =705629a(28) =808231a(29) =921631