|
Search: id:A122195
|
|
|
| A122195 |
|
Numbers that are the sum of exactly 3 sets of Fibonacci numbers. |
|
+0
5
|
|
| 8, 11, 13, 14, 18, 19, 22, 23, 30, 31, 36, 38, 49, 51, 59, 62, 80, 83, 96, 101, 130, 135, 156, 164, 211, 219, 253, 266, 342, 355, 410, 431, 554, 575, 664, 698, 897, 931, 1075, 1130, 1452, 1507, 1740, 1829, 2350, 2439, 2816, 2960, 3803, 3947, 4557, 4790, 6154
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
M. Bicknell-Johnson & D.C. Fielder, 'The number of Representations of N Using Distinct Fibonacci Numbers, Counted by Recursive Formulas' Fibonacci Quart. 37.1 (1999) pgs 47 ff
|
|
LINKS
|
Ron Knott Sumthing about Fibonacci Numbers
|
|
FORMULA
|
GF: (8+3*x+2*x^2+x^3-4*x^4-2*x^5+x^6-5*x^8-3*x^9)/(x^9-x^8+x^5-x^4-x+1). {a(n)}={ series starting [8,8,11,11,13,13,18,19] then a(n)=a(n-4)+a(n-8)+1,n>7} a(0)=8, a(1)=11, a(2)=13, a(3)=18, then: a(4n)=A022318(n+3) = 2 A00045(n+5) + A000045(n+3) - 1,n>=1 a(4n+1)=A022406(n+2) = 4 A000045(n+4) - 1,n>=1 a(4n+2)=A022308(n+4)= 2 A000045(n+4) + A000045(n+6) - 1,n>=1, a(4n+3) = 3 A000045(n+4) - 1,n>=1
|
|
EXAMPLE
|
8 is the sum of only 3 sets of Fibonacci numbers: {8}, {3,5} and {1,2,5}
11 is the sum of only {3,8}, {1,2,8}, {1,2,3,5}
|
|
MAPLE
|
first N terms: series((8+3*x+2*x^2+x^3-4*x^4-2*x^5+x^6-5*x^8-3*x^9)/(x^9-x^8+x^5-x^4-x+1), x, N);
|
|
CROSSREFS
|
Cf. A000045, A000071, A013583, A000119, A122194.
Sequence in context: A077060 A123939 A134787 this_sequence A064153 A106670 A153039
Adjacent sequences: A122192 A122193 A122194 this_sequence A122196 A122197 A122198
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Ron Knott (enquiry(AT)ronknott.com), Aug 25 2006, corrected Aug 29 2006
|
|
|
Search completed in 0.002 seconds
|
