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A060472
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Smallest positive a(n) such that the number of solutions to a(n)=a(j)+a(k), j<k<n is four or less.
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7
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 23, 25, 27, 29, 31, 36, 38, 40, 42, 44, 51, 53, 55, 57, 64, 66, 68, 70, 72, 77, 79, 81, 83, 85, 92, 94, 96, 98, 105, 107, 109, 111, 118, 120, 122, 124, 126, 131, 133, 135, 137, 139, 146, 148, 150, 152, 159, 161, 163
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OFFSET
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1,2
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COMMENTS
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Numbers {1,3,10,12,14,16,18,23,25,27,29,31,38,40,42,44,51,53} mod 54 plus {2,4,5,6,7,8,9,20,36}.
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-18) - a(n-19) for n > 40.
G.f.: x*(5*x^39 - 3*x^38 + 3*x^34 - x^33 + 5*x^29 + x^27 + x^26 + 6*x^25 + x^24 + x^23 + x^22 + x^21 + 4*x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + 3*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/(x^19 - x^18 - x + 1). (End)
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EXAMPLE
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12 is in the sequence since it is 5+7, 4+8, 3+9 and 2+10 but no other sum of two distinct terms.
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MATHEMATICA
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f[s_List, j_Integer] := Block[{cnt, k = s[[-1]] + 1, ss = Plus @@@ Subsets[s, {j}]}, While[ cnt = Count[ss, k]; cnt == 0 || cnt > 4, k++]; Append[s, k]]; Nest[f[#, 2] &, {1, 2}, 70] (* Robert G. Wilson v, Jul 05 2014 *)
CoefficientList[Series[(5 x^39 - 3 x^38 + 3 x^34 - x^33 + 5 x^29 + x^27 + x^26 + 6 x^25 + x^24 + x^23 + x^22 + x^21 + 4 x^20 + x^19 + x^18 + 2 x^17 + 2 x^16 + 3 x^15 + 2 x^14 + 2 x^13 + 2 x^12 + 2 x^11 + 2 x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) / (x^19 - x^18 - x + 1), {x, 0, 100}], x] (* Vincenzo Librandi, Feb 22 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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