Number of polynomials of height n: a(1)=1, a(2)=1, a(3)=4, a(n) = 2*a(n-1) + a(n-2) + 2 for n >= 4.

Terms

a(0) =1a(1) =1a(2) =4a(3) =11a(4) =28a(5) =69a(6) =168a(7) =407a(8) =984a(9) =2377a(10) =5740a(11) =13859a(12) =33460a(13) =80781a(14) =195024a(15) =470831a(16) =1136688a(17) =2744209a(18) =6625108a(19) =15994427a(20) =38613964a(21) =93222357a(22) =225058680a(23) =543339719a(24) =1311738120a(25) =3166815961a(26) =7645370044a(27) =18457556051a(28) =44560482148a(29) =107578520349