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

1,3

Links

Table of n, a(n) for n=1..11.

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

Formula

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

Example

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).

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 *)

Prog

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

Crossrefs

Sequence in context: A197974 A208985 A333738 * A254429 A298945 A027303

Adjacent sequences: A114790 A114791 A114792 * A114794 A114795 A114796

Keyword

nonn

Author

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

Status

approved