

A213437


Nonlinear recurrence: a(n) = a(n1) + (a(n1)+1)*Product_{j=1..n2} a(j).
(Formerly N1082)


6




OFFSET

1,2


COMMENTS

This sequence was going to be included in the AhoSloane paper, but was omitted from the published version.
It appears that the sequence becomes periodic mod 10^k for any k, with period 3. The last digits are (1,3,7) repeated. Modulo 10^5 the sequence enters the cycle (56703, 79007, 23231) after the first 10 terms.  M. F. Hasler, Jul 23 2012. See also A214635, A214636.


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).


LINKS

Table of n, a(n) for n=1..9.
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429437. [Includes many similar sequences, although not this one.]


FORMULA

a(n) = a(n1)+(a(n1)+1)*(a(n1)a(n2))*a(n2)/(a(n2)+1).  Johan de Ruiter, Jul 23 2012
a(2+3k) = 9007 (mod 10^4) for all k>0.  M. F. Hasler, Jul 23 2012
a(n) ~ c^(2^n), where c = A076949 = 1.2259024435287485386279474959130085213212293209696612823177009... .  Vaclav Kotesovec, May 06 2015
a(n) = A001699(n)/A001699(n1); a(n+1)  a(n) = A001699(n) + A001699(n1); a(n) = A003095(n) + A003095(n1).  Peter Bala, Feb 03 2017


MAPLE

A213437 := proc(n)
if n = 1 then 1;
else procname(n1)+(1+procname(n1))*mul(procname(j), j=1..n2);
end if;
end proc: # R. J. Mathar, Jul 23 2012


MATHEMATICA

RecurrenceTable[{a[n] == a[n1]+(a[n1]+1)*(a[n1]a[n2])*a[n2]/(a[n2]+1), a[1]==1, a[2]==3}, a, {n, 1, 10}] (* Vaclav Kotesovec, May 06 2015 *)


PROG

(PARI) a=[1]; for(n=1, 11, a=concat(a, a[n] + (a[n]+1) * prod(k=1, n1, a[k] ))); a \\  M. F. Hasler, Jul 23 2012


CROSSREFS

Cf. A076949, A214635, A214636, A003095, A001699.
Sequence in context: A121810 A081475 A123212 * A070231 A263049 A167917
Adjacent sequences: A213434 A213435 A213436 * A213438 A213439 A213440


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jun 11 2012


EXTENSIONS

Definition recovered by Johan de Ruiter, Jul 23 2012


STATUS

approved



