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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

R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992

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 A328727

Adjacent sequences:  A007083 A007084 A007085 * A007087 A007088 A007089

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 26 08:06 EDT 2020. Contains 338027 sequences. (Running on oeis4.)