A117546 Number of representations of n as a sum of distinct tribonacci numbers (A000073).

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

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, Tribonacci Number.

Eric Weisstein's World of Mathematics, 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