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A244749 0-additive sequence: a(n) is the smallest number larger than a(n-1) that is not the sum of any subset of earlier terms, starting with initial values {2, 5}. 1
2, 5, 6, 9, 10, 28, 29, 85, 86, 256, 257, 769, 770, 2308, 2309, 6925, 6926, 20776, 20777, 62329, 62330, 186988, 186989, 560965, 560966, 1682896, 1682897, 5048689, 5048690, 15146068, 15146069, 45438205, 45438206, 136314616, 136314617, 408943849, 408943850, 1226831548, 1226831549 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence differs from A003664.

REFERENCES

R. K. Guy, "s-Additive sequences," preprint, 1994.

LINKS

Table of n, a(n) for n=1..39.

S. R. Finch, Are 0-additive sequences always regular?, Amer. Math. Monthly, 99 (1992), 671-673.

Index entries for linear recurrences with constant coefficients, signature (-1,3,3).

FORMULA

a(2n) = 4a(2n - 2) - 3a(2n - 4) and a(2n +1) = a(2n) +1, for n>2.

a(n) = -a(n-1) + 3*a(n-2) + 3*a(n-3) for n>6. - Colin Barker, Jul 11 2014

G.f.: x*(7*x^5+14*x^4+6*x^3-5*x^2-7*x-2) / ((x+1)*(3*x^2-1)). - Colin Barker, Jul 11 2014

EXAMPLE

The numbers 11-27 are not in the sequence since some combination of the previous terms add to it. example 17=2+5+10.

The number 28 however is a term since no combination of the previous terms cannot be found which sum to 28.

MATHEMATICA

f[s_List] := f[n] = Block[{k = s[[-1]] + 1, ss = Union[ Plus @@@ Subsets[s]]}, While[ MemberQ[ss, k], k++]; Append[s, k]]; Nest[ f[#] &, {2, 5}, 20] (* or *)

b = LinearRecurrence[{4, -3}, {9, 28}, 18]; Join[{2, 5, 6}, Riffle[b, b + 1]]

Join[{2, 5, 6}, LinearRecurrence[{-1, 3, 3}, {9, 10, 28}, 36]] (* Ray Chandler, Aug 03 2015 *)

PROG

(PARI) Vec(x*(7*x^5+14*x^4+6*x^3-5*x^2-7*x-2)/((x+1)*(3*x^2-1)) + O(x^100)) \\ Colin Barker, Jul 11 2014

CROSSREFS

Cf. A003662, A003663, A005408, A026471, A026474, A033627, A051039, A051040, A244151, A244750.

Cf. A060469 - A060472.

Sequence in context: A078632 A122701 A032925 * A166087 A281902 A153143

Adjacent sequences:  A244746 A244747 A244748 * A244750 A244751 A244752

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane and Robert G. Wilson v, Jul 05 2014

STATUS

approved

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Last modified June 19 23:01 EDT 2019. Contains 324222 sequences. (Running on oeis4.)