

A247184


a(0) = 0. a(n) is the number of distinct sums of two elements in [a(0), ... a(n1)] chosen without replacement.


1



0, 0, 1, 2, 4, 7, 11, 15, 20, 26, 32, 40, 48, 57, 65, 73, 81, 90, 98, 106, 114, 123, 132, 147, 157, 170, 190, 202, 223, 236, 251, 270, 291, 314, 338, 361, 380, 398, 421, 443, 471, 495, 520, 544, 567, 592, 616, 639, 663, 692, 720, 749, 781, 819, 852, 885, 913, 948, 987, 1023, 1055, 1088
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

a(n) <= A000217(n)n.
Without replacement means that a(i)+a(i) is not a valid sum to include. However, if a(i) = a(j), a(i)+a(j) is still a valid sum to include because they have different indices.
If you include a(i)+a(i) (i.e., with replacement) as a valid sum, the sequence becomes 0, 1, 3, 6, 9, 12, ... = 0, 1, followed by A008585(n) for n > 0.
a(i)+a(j) and a(j)+a(i) are regarded as the same for all indices i and j.


LINKS

Table of n, a(n) for n=0..61.


EXAMPLE

a(1) gives the number of distinct sums of two elements of [0]. There aren't two elements so a(1) = 0.
a(2) gives the number of distinct sums of two elements of [0,0]. There is only 1 sum, 0, so a(2) = 1.
a(3) gives the number of distinct sums of two elements of [0,0,1]. There are 2 distinct possible sums 0 and 1, so a(3) = 2.
a(4) gives the number of distinct sums of two elements of [0,0,1,2]. There are 4 distinct possible sums {0, 1, 2, 3}, so a(4) = 4.


PROG

(PARI) v=[0]; n=1; while(n<75, w=[]; for(i=1, #v, for(j=i+1, #v, w=concat(w, v[i]+v[j]))); v=concat(v, #vecsort(w, , 8)); n++); v


CROSSREFS

Cf. A000217, A008585, A247185.
Sequence in context: A198759 A078617 A199085 * A025703 A025709 A036700
Adjacent sequences: A247181 A247182 A247183 * A247185 A247186 A247187


KEYWORD

nonn


AUTHOR

Derek Orr, Nov 22 2014


STATUS

approved



