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A213437
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Nonlinear recurrence: a(n) = a(n-1) + (a(n-1)+1)*Product_{j=1..n-2} a(j).
(Formerly N1082)
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6
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OFFSET
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1,2
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COMMENTS
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This sequence was going to be included in the Aho-Sloane 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.
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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LINKS
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FORMULA
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a(n) = a(n-1)+(a(n-1)+1)*(a(n-1)-a(n-2))*a(n-2)/(a(n-2)+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
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MAPLE
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if n = 1 then 1;
else procname(n-1)+(1+procname(n-1))*mul(procname(j), j=1..n-2);
end if;
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MATHEMATICA
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RecurrenceTable[{a[n] == a[n-1]+(a[n-1]+1)*(a[n-1]-a[n-2])*a[n-2]/(a[n-2]+1), a[1]==1, a[2]==3}, a, {n, 1, 10}] (* Vaclav Kotesovec, May 06 2015 *)
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PROG
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(PARI) a=[1]; for(n=1, 11, a=concat(a, a[n] + (a[n]+1) * prod(k=1, n-1, a[k] ))); a \\ - M. F. Hasler, Jul 23 2012
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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