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Search: id:A117546
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| A117546 |
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Number of representations of n as a sum of distinct tribonacci numbers (A000073). |
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+0
1
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| 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 2, 2, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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It can be shown that, like the Fibonacci numbers, the tribonacci numbers are complete; that is, a(n)>0 for all n. There is always a representation, free of three consecutive tribonacci numbers, which is analogous to the Zeckendorf representation of Fibonacci numbers. See A003726.
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LINKS
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Eric Weisstein's World of Mathematics, Math World: Tribonacci Number
Eric Weisstein's World of Mathematics, Math World: Zeckendorf Representation
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EXAMPLE
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a(14)=2 because 14 is both 13+1 and 7+4+2+1.
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MATHEMATICA
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tr={1, 2, 4, 7, 13, 24, 44, 81, 149}; len=tr[[ -1]]; cnt=Table[0, {len}]; Do[v=IntegerDigits[k, 2, Length[tr]]; s=Dot[tr, v]; If[s<=len, cnt[[s]]++ ], {k, 2^(Length[tr])-1}]; cnt
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CROSSREFS
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Cf. A000119 (number of representations of n as a sum of distinct Fibonacci numbers).
Adjacent sequences: A117543 A117544 A117545 this_sequence A117547 A117548 A117549
Sequence in context: A095684 A064531 A037829 this_sequence A096811 A082478 A083382
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KEYWORD
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easy,nonn
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AUTHOR
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T. D. Noe and Jonathan Vos Post (noe(AT)sspectra.com), Mar 28 2006
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