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a(1) = a(2) = a(3) = a(4) = 1. For n>= 5, a(n) = a(n-1)*a(n-4) + a(n-2)*a(n-3).
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%I #7 Feb 23 2023 16:58:37

%S 1,1,1,1,2,3,5,11,37,166,1237,19749,936055,179814643,240916863586,

%T 4926183534613279,4654499108310829164143,

%U 838133896191338105830469104443,201943518452400520392903690464302135967495,994814736615560793049792416556718062880283217474796953454

%N a(1) = a(2) = a(3) = a(4) = 1. For n>= 5, a(n) = a(n-1)*a(n-4) + a(n-2)*a(n-3).

%t nxt[{a_,b_,c_,d_}]:={b,c,d,a*d+b*c}; NestList[nxt,{1,1,1,1},20][[;;,1]] (* _Harvey P. Dale_, Feb 23 2023 *)

%o (PARI) a(n)=if(n<5,1,a(n-1)*a(n-4) + a(n-2)*a(n-3)) (Klasen)

%K easy,nonn

%O 1,5

%A _Leroy Quet_, Nov 01 2005

%E More terms from Lambert Klasen (lambert.klasen(AT)gmx.net), Nov 06 2005