A114793 a(1) = a(2) = 1; for n>2, a(n) = a(n-2)^3 + a(n-1)^2.

1, 1, 2, 5, 33, 1214, 1509733, 2281082919633, 5203342727366374356990526, 27074775538448408469117040958804384971249439965813, 733043470457364306745565389055274337169526356099299839341244874661931850021760795731279812250002545

Offset: 1

Author

Stephen T. Rowe (EbolaPox(AT)gmail.com), Feb 18 2006

Keywords

• nonn

Examples

			a(4) = sum of the cube of a(2) plus the square of a(3) = cube of 1 + the square of 2, resulting in 1 + 4 = 5. The next term is a(3)^3 + a(4)^2 = (2^3) + 5^2 = 33 = a(5).
		

Links

• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Programs

Mathematica

Nest[Append[#,Last[#]^2+#[[-2]]^3]&,{1,1},10]  (* Harvey P. Dale, Apr 17 2011 *)
nxt[{a_,b_}]:={b,a^3+b^2}; NestList[nxt,{1,1},10][[All,1]] (* Harvey P. Dale, Dec 04 2018 *)

Python

a,b = 0,1
for k in range(8):
    print(b, end=", ")
    a,b = b, a*a*a + b*b

Formula

a(n) ~ c^(2^n), where c = 1.117568080436159210016482629050645172893788101196409851633874670767953... . - Vaclav Kotesovec, Dec 18 2014