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A338921 a(0)=1, a(n) for n >= 1 is the number of distinct sums of two elements in [a(0), ..., a(n-1)], chosen without replacement. 0
1, 0, 1, 2, 3, 5, 8, 12, 17, 22, 28, 35, 43, 52, 60, 69, 77, 86, 92, 103, 112, 123, 137, 151, 168, 180, 194, 204, 224, 245, 261, 280, 301, 318, 335, 352, 369, 387, 413, 433, 459, 482, 507, 528, 552, 586, 614, 638, 669, 701, 733, 761, 791, 824, 855, 885, 917, 952, 985, 1020 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) <= A000217(n)-n for n >= 1.

Without replacement means a(i)+a(i) is not included. However, if a(i)=a(j), a(i)+a(j) still counts because they have two different indices. If you include a(i)+a(i), the sequence becomes A000012 (all ones).

If you include the distinct sums between 3 elements and more, you arrive at the sequence 1, 0, followed by A000079 (2^n).

Same rule as in A247184, but with a(0)=1.

LINKS

Table of n, a(n) for n=0..59.

EXAMPLE

a(1) gives the number of distinct sums between two elements of [1]. There aren't two elements so a(1)=0.

a(2) gives the number of distinct sums between two elements of [1,0]. The only sum are 1+0, so a(2) = 1.

a(3) gives the number of distinct sums between two elements of [1,0,1]. The two sums are 1+0 and 1+1 so a(3)=2.

MAPLE

s:= proc(n) option remember; `if`(n=0, {},

      {s(n-1)[], seq(a(i)+a(n), i=0..n-1)})

    end:

a:= proc(n) option remember;

      `if`(n=0, 1, nops(s(n-1)))

    end:

seq(a(n), n=0..60);  # Alois P. Heinz, Nov 16 2020

MATHEMATICA

a[0] = 1; a[1] = 0;

a[n_Integer?Positive] := a[n] = Length[Union[Total[Subsets[Array[a, n, 0], {2}], {2}]]];

Array[a, 61, 0] (* Jan Mangaldan, Nov 23 2020 *)

PROG

(PARI) my(v=[1], w=[], n=1); while(n<75, for(i=2, #v, w=concat(w, v[i-1]+v[#v])); w=vecsort(w, , 8); v=concat(v, #w); n++); v

CROSSREFS

Cf. A000217, A000012, A247184, A247185.

Sequence in context: A028955 A246321 A104664 * A333343 A022856 A089071

Adjacent sequences:  A338918 A338919 A338920 * A338922 A338923 A338924

KEYWORD

nonn

AUTHOR

Derek Orr, Nov 15 2020

STATUS

approved

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Last modified July 26 15:49 EDT 2021. Contains 346294 sequences. (Running on oeis4.)