A039941 Alternately add and multiply.

0, 1, 1, 1, 2, 2, 4, 8, 12, 96, 108, 10368, 10476, 108615168, 108625644, 11798392572168192, 11798392680793836, 139202068568601556987554268864512, 139202068568601568785946949658348, 19377215893777651167043206536157390321290709180447278572301746176

Offset

0,5

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..27

A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437, alternative link.

Formula

a(2n) = a(2n-1) + a(2n-2); a(2n+1) = a(2n-1)*a(2n); a(0) = 0; a(1) = 1

a(n) = {a(n-1) + a(n-2), n even, a(n-1)*a(n-2), n odd}; a(0)=0; a(1)=1.

Mathematica

nxt[{n_, a_, b_}]:={n+1, b, If[EvenQ[n], a+b, a*b]}; Join[{0}, Transpose[ NestList[ nxt, {0, 0, 1}, 20]][[3]]] (* Harvey P. Dale, Aug 23 2013 *)

Prog

(PARI) a(n)=if(n<2, n>0, if(n%2, a(n-1)*a(n-2), a(n-1)+a(n-2)))
(Haskell)
a039941 n = a039941_list !! (n-1)
a039941_list = 0 : 1 : zipWith3 ($)
   (cycle [(+), (*)]) a039941_list (tail a039941_list)
-- Reinhard Zumkeller, May 07 2012

Crossrefs

A001696(n)=A039941(2*n), A001697(n)=A039941(2*n+1).

Cf. A077753

Sequence in context: A079092 A323865 A104700 * A036761 A042979 A000018

Adjacent sequences: A039938 A039939 A039940 * A039942 A039943 A039944

Keyword

easy,nonn,nice

Author

Walter Carlini

Extensions

Additional comments from Michael Somos, May 19 2000

One more term from Harvey P. Dale, Aug 23 2013

Status

approved