OFFSET
1,2
COMMENTS
Numbers {1,3,8,10} mod 11 plus {2,4,5,6,7,16}. Note that while the cases for "zero", "one", "two" and "four" essentially involve a third of the natural numbers, this case for "three" involves 4/11.
FORMULA
From Chai Wah Wu, Feb 21 2018: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 17.
G.f.: x*(2*x^16 + x^12 + x^11 + x^10 + x^9 + x^8 + x^3 + x^2 + x + 1)/(x^5 - x^4 - x + 1). (End)
EXAMPLE
12 is in the sequence since it is 5+7, 4+8 and 2+10 but no other sum of two distinct terms.
MATHEMATICA
f[s_List, j_Integer] := Block[{cnt, k = s[[-1]] + 1, ss = Plus @@@ Subsets[s, {j}]}, While[ cnt = Count[ss, k]; cnt == 0 || cnt > 3, k++]; Append[s, k]]; Nest[f[#, 2] &, {1, 2}, 70] (* Robert G. Wilson v, Jul 05 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Mar 15 2001
STATUS
approved