Number of length 2+2 0..n arrays with the medians of every three consecutive terms nondecreasing.

Terms

a(0) =14a(1) =67a(2) =204a(3) =485a(4) =986a(5) =1799a(6) =3032a(7) =4809a(8) =7270a(9) =10571a(10) =14884a(11) =20397a(12) =27314a(13) =35855a(14) =46256a(15) =58769a(16) =73662a(17) =91219a(18) =111740a(19) =135541a(20) =162954a(21) =194327a(22) =230024a(23) =270425a(24) =315926a(25) =366939a(26) =423892a(27) =487229a(28) =557410a(29) =634911