a(n) = spt(5n+4)/5 where spt(n) = A092269(n).

Terms

a(0) =2a(1) =16a(2) =88a(3) =364a(4) =1309a(5) =4126a(6) =11992a(7) =32368a(8) =82590a(9) =200487a(10) =467152a(11) =1049224a(12) =2283364a(13) =4829302a(14) =9959035a(15) =20069790a(16) =39612612a(17) =76703340a(18) =145945332a(19) =273224940a(20) =503888206a(21) =916373028a(22) =1644925432a(23) =2916814954a(24) =5113148026a(25) =8866911378a(26) =15220453704