a(n) is the number of perfect matchings of an edge-labeled 2 X (2n+1) Mobius grid graph.

Terms

a(0) =3a(1) =6a(2) =13a(3) =31a(4) =78a(5) =201a(6) =523a(7) =1366a(8) =3573a(9) =9351a(10) =24478a(11) =64081a(12) =167763a(13) =439206a(14) =1149853a(15) =3010351a(16) =7881198a(17) =20633241a(18) =54018523a(19) =141422326a(20) =370248453a(21) =969323031a(22) =2537720638a(23) =6643838881a(24) =17393796003a(25) =45537549126a(26) =119218851373a(27) =312119004991a(28) =817138163598