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A108225
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a(0) = 0, a(1) = 2; for n >= 2, a(n) = (a(n-1)+a(n-2))*(a(n-1)-a(n-2)+1)/2.
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0, 2, 3, 5, 12, 68, 2280, 2598062, 3374961778893, 5695183504492614029263280, 16217557574922386301420536972254869595782763547562
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| From a posting by Antreas P. Hatzipolakis to the Yahoo news group "Hyacinthos", circa Jun 10 2005
The next term has 99 digits [from Harvey P. Dale, Jun3 09 2011]
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FORMULA
| Conjecture: a(n)=A006894(n)+1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 23 2007
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MAPLE
| F:=proc(n) option remember; if n <= 1 then RETURN(2*n) fi; (F(n-1)+F(n-2))*(F(n-1)-F(n-2)+1)/2; end;
a[ -2]:=-2:a[ -1]:=0:a[0]:=1:for n from 1 to 50 do a[n]:=binomial(a[n-1]+2, 2) od: seq(a[n]+2, n=-2..8); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 08 2007
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MATHEMATICA
| RecurrenceTable[{a[0]==0, a[1]==2, a[n]==(a[n-1]+a[n-2])(a[n-1]- a[n-2]+1)/2}, a[n], {n, 15}] (* From Harvey P. Dale, June 09 2011 *)
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CROSSREFS
| First differences give A103410.
Sequence in context: A008323 A000997 A107475 * A193064 A133832 A061488
Adjacent sequences: A108222 A108223 A108224 * A108226 A108227 A108228
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 16 2005
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EXTENSIONS
| The next term is too large to include.
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