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A006893
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Smallest number whose representation requires n triangular numbers with greedy algorithm; also number of 1-2 rooted trees of height n.
(Formerly M1533)
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10
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OFFSET
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1,2
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REFERENCES
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M. Abert and P. Diaconis, paper in preparation, 2002.
D. Parisse, The Tower of Hanoi and the Stern-Brocot-Array, Thesis, Munich, 1997.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n+1) = a(n)*(a(n)+3)/2, a(1)=1.
a(0) = 1, a(n) = Sum_{i=0..n-1} t(a(i)), where t(n)=n*(n+1)/2. - Jon Perry, Feb 14 2004
a(n) ~ 2 * c^(2^n), where c = 1.16007248510653786919452141287945841802404855231102953089... . - Vaclav Kotesovec, Dec 17 2014
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MAPLE
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MATHEMATICA
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RecurrenceTable[{a[1] == 1, a[n] == a[n-1]*(a[n-1] + 3)/2}, a[n], {n, 10}] (* Vaclav Kotesovec, Dec 17 2014 *)
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PROG
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(PARI) a=vector(20); a[1]=1; for(n=2, #a, a[n]=a[n-1]*(a[n-1]+3)/2); a \\ Altug Alkan, Apr 04 2018
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CROSSREFS
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Where records occur in A057945, n >= 1.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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