a(n) = ((5+sqrt(2))*(1+sqrt(2))^n + (5-sqrt(2))*(1-sqrt(2))^n)/2.

Terms

a(0) =5a(1) =7a(2) =19a(3) =45a(4) =109a(5) =263a(6) =635a(7) =1533a(8) =3701a(9) =8935a(10) =21571a(11) =52077a(12) =125725a(13) =303527a(14) =732779a(15) =1769085a(16) =4270949a(17) =10310983a(18) =24892915a(19) =60096813a(20) =145086541a(21) =350269895a(22) =845626331a(23) =2041522557a(24) =4928671445a(25) =11898865447a(26) =28726402339a(27) =69351670125