login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007086 Next term is uniquely the sum of 3 earlier terms.
(Formerly M0756)
10
1, 2, 3, 6, 9, 10, 11, 12, 28, 29, 30, 53, 56, 57, 80, 82, 104, 105, 107, 129, 130, 132, 154, 155, 157, 179, 180, 182, 204, 205, 207, 229, 230, 232, 254, 255, 257, 279, 280, 282, 304, 305, 307, 329, 330, 332, 354, 355, 357, 379, 380, 382, 404, 405, 407, 429 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(1)=1, a(2)=2, a(3)=3, for n>3, a(n) = least number which is a unique sum of three distinct earlier terms.  Written this way, we see that this is to 3 as Ulam number A002858 is to 2. - Jonathan Vos Post

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

M. C. Wunderlich, The improbable behavior of Ulam's summation sequence, pp. 249-257 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: (22*x^18 -21*x^17 +x^16 -2*x^13 -7*x^12 -15*x^9 +2*x^8 +2*x^7 -2*x^5 -2*x^4 -x^3 -x^2 -x) / (-x^4+x^3+x-1).  Conjectured and verified for n<=1100 - Alois P. Heinz, Jan 04 2011

EXAMPLE

13 through 27 are not in the sequence because of nonuniqueness: 1+3+9=1+2+10=13, 1+3+10=2+3+9=14, 1+2+12=2+3+10=15, 1+6+9=2+3+11=16, 1+7+9=2+6+9=17, 3+6+9=1+6+11=18, 1+6+12=2+6+11=19, 1+9+10=2+6+12=20, 1+9+11=2+9+10=21, 1+10+11=2+9+11=22, 2+9+12=3+9+11=23, 1+11+12=3+9+12=24, 3+10+12=6+9+10=25, 3+11+12=6+9+11=26, 6+9+12=6+10+11=27. - Jonathan Vos Post

MATHEMATICA

Clear[a]; a[n_ /; n <= 3] := n; a[n_] := a[n] = (t = Table[a[i]+a[j]+a[k], {i, 1, n-3}, {j, i+1, n-2}, {k, j+1, n-1}] // Flatten; Complement[Select[t // Tally, #[[2]] == 1&][[All, 1]], Array[a, n-1]] // Sort // First); Array[a, 56] (* Jean-Fran├žois Alcover, Mar 11 2014 *)

CROSSREFS

Cf. A002858.

Sequence in context: A140783 A094351 A061910 * A047404 A133555 A032938

Adjacent sequences:  A007083 A007084 A007085 * A007087 A007088 A007089

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 29 06:34 EDT 2017. Contains 284250 sequences.