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A117546 Number of representations of n as a sum of distinct tribonacci numbers (A000073). 5
1, 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; text; internal format)
OFFSET

0,8

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.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Math World: Tribonacci Number

Eric Weisstein's World of Mathematics, Math World: Zeckendorf Representation

EXAMPLE

a(14)=2 because 14 is both 13+1 and 7+4+2+1.

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

PROG

(Haskell)

a117546 = p $ drop 3 a000073_list where

   p _  0     = 1

   p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m

-- Reinhard Zumkeller, Apr 13 2014

CROSSREFS

Cf. A000119 (number of representations of n as a sum of distinct Fibonacci numbers).

Cf. A240844.

Sequence in context: A185646 A037829 A270992 * A274196 A096811 A082478

Adjacent sequences:  A117543 A117544 A117545 * A117547 A117548 A117549

KEYWORD

easy,nonn

AUTHOR

T. D. Noe and Jonathan Vos Post, Mar 28 2006

EXTENSIONS

a(0)=1 added and offset changed by Reinhard Zumkeller, Apr 13 2014

STATUS

approved

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Last modified September 22 00:42 EDT 2020. Contains 337276 sequences. (Running on oeis4.)