A Pell related sequence.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =14a(5) =50a(6) =199a(7) =749a(8) =2892a(9) =11028a(10) =42301a(11) =161799a(12) =619706a(13) =2372006a(14) =9081955a(15) =34767953a(16) =133109592a(17) =509594856a(18) =1950956857a(19) =7469077707a(20) =28594853414a(21) =109473250778a(22) =419110475455