J(n)^2+J(n+1)^2, with J(n) the Jacobsthal number A001045(n).

Terms

a(0) =1a(1) =2a(2) =10a(3) =34a(4) =146a(5) =562a(6) =2290a(7) =9074a(8) =36466a(9) =145522a(10) =582770a(11) =2329714a(12) =9321586a(13) =37280882a(14) =149134450a(15) =596515954a(16) =2386107506a(17) =9544342642a(18) =38177545330a(19) =152709831794a(20) =610840026226