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 A001696 a(n) = a(n-1)*(1 + a(n-1) - a(n-2)), a(0) = 0, a(1) = 1. (Formerly M1268 N0487) 4
 0, 1, 2, 4, 12, 108, 10476, 108625644, 11798392680793836, 139202068568601568785946949658348, 19377215893777651167043206536157529523359277782016064519251404524 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also, numbers remaining after the following sieving process: In step 1, keep all numbers of the set N={0,1,2,...}. In step 2, keep only every second number after a(2)=2: N'={0,1,2,4,6,8,10,...}. In step 3, keep every 4th of the numbers following a(3)=4, N"={0,1,2,4,12,20,28,...}. In step 4, keep every 12th of the numbers beyond a(4)=12: {0,1,2,4,12,108,204,...}. In step 5, keep every 108th of the numbers beyond a(5)=108: {0,1,2,4,12,108,10476,...}, and so on. The next "gap" a(n+1)-a(n) is always a(n) times the former gap, i.e., a(n+1)-a(n) = a(n)*(a(n)-a(n-1)). [From M. F. Hasler, Oct 28 2010] REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS John Cerkan, Table of n, a(n) for n = 0..13 A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437. FORMULA a(n) ~ c^(2^n), where c = 1.15552822483840350150537253088299651035583896919522349372370013726451673646... . - Vaclav Kotesovec, May 21 2015 MATHEMATICA a = 0; a = 1; a[n_] := a[n] = a[n-1]*(1 + a[n-1] - a[n-2]); Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Jul 02 2013 *) PROG (PARI) a(n)=if(n<2, n>0, a(n-1)*(1+a(n-1)-a(n-2))) (Haskell) a001696 n = a001696_list !! n a001696_list = 0 : 1 : zipWith (-)    (zipWith (+) a001696_list' \$ map (^ 2) a001696_list')    (zipWith (*) a001696_list a001696_list')    where a001696_list' = tail a001696_list -- Reinhard Zumkeller, Apr 29 2013 CROSSREFS a(n)=A039941(2*n); first difference sequence of this sequence is A001697. - Michael Somos, May 19 2000 Sequence in context: A038791 A327563 A326950 * A276534 A326969 A304986 Adjacent sequences:  A001693 A001694 A001695 * A001697 A001698 A001699 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 14 02:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)