Number of length 3+2 0..n arrays with the medians of every three consecutive terms nondecreasing.

Terms

a(0) =24a(1) =162a(2) =632a(3) =1827a(4) =4368a(5) =9156a(6) =17424a(7) =30789a(8) =51304a(9) =81510a(10) =124488a(11) =183911a(12) =264096a(13) =370056a(14) =507552a(15) =683145a(16) =904248a(17) =1179178a(18) =1517208a(19) =1928619a(20) =2424752a(21) =3018060a(22) =3722160a(23) =4551885a(24) =5523336a(25) =6653934a(26) =7962472a(27) =9469167a(28) =11195712a(29) =13165328