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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
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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; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| 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
| 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
| a(14)=2 because 14 is both 13+1 and 7+4+2+1.
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MATHEMATICA
| 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
| Cf. A000119 (number of representations of n as a sum of distinct Fibonacci numbers).
Sequence in context: A205565 A064531 A037829 * A096811 A082478 A083382
Adjacent sequences: A117543 A117544 A117545 * A117547 A117548 A117549
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KEYWORD
| easy,nonn
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AUTHOR
| T. D. Noe and Jonathan Vos Post (noe(AT)sspectra.com), Mar 28 2006
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