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A122195 Numbers that are the sum of exactly 3 sets of Fibonacci numbers. 4
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; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..53.

Ron Knott Sumthing about Fibonacci Numbers

FORMULA

G.f.: (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+1);

CROSSREFS

Cf. A000045, A000071, A013583, A000119, A122194.

Sequence in context: A134787 A249104 A191887 * A064153 A106670 A247463

Adjacent sequences:  A122192 A122193 A122194 * A122196 A122197 A122198

KEYWORD

nonn

AUTHOR

Ron Knott, Aug 25 2006, corrected Aug 29 2006

STATUS

approved

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Last modified April 28 16:04 EDT 2017. Contains 285578 sequences.