A060472 Smallest positive a(n) such that the number of solutions to a(n)=a(j)+a(k), j<k<n is four or less.

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

Offset

1,2

Comments

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}.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Formula

From Chai Wah Wu, Feb 21 2018: (Start)

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)

Example

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.

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 > 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 *)

Crossrefs

Cf. A033627, A060469, A060470, A060471, A060472.

Sequence in context: A083292 A122618 A033062 * A130514 A130232 A103969

Adjacent sequences: A060469 A060470 A060471 * A060473 A060474 A060475

Keyword

nonn

Author

Henry Bottomley, Mar 15 2001

Status

approved