|
|
A117546
|
|
Number of representations of n as a sum of distinct tribonacci numbers (A000073).
|
|
9
|
|
|
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
|
|
|
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
|
|
CROSSREFS
|
Cf. A000119 (number of representations of n as a sum of distinct Fibonacci numbers).
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|