A060470
Smallest positive a(n) such that number of solutions to a(n)=a(j)+a(k) j
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 19, 24, 26, 28, 33, 35, 37, 42, 44, 46, 51, 53, 55, 60, 62, 64, 69, 71, 73, 78, 80, 82, 87, 89, 91, 96, 98, 100, 105, 107, 109, 114, 116, 118, 123, 125, 127, 132, 134, 136, 141, 143, 145, 150, 152, 154, 159, 161, 163, 168, 170
Offset: 1
Examples
12 is in the sequence since it is 4+8 and 2+10 but no other sum of two distinct terms.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..3000
- Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
Programs
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Magma
I:=[1,2,3,4,5,6,8,10,12,15,17,19,24]; [n le 13 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Feb 22 2018
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Magma
[n le 9 select Floor(n^2/12+n/2+3/4) else 2*n+3*Floor(n/3+2/3)-17: n in [1..65]]; // Bruno Berselli, Feb 22 2018
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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 > 2, k++]; Append[s, k]]; Nest[f[#, 2] &, {1, 2}, 70] (* Robert G. Wilson v, Jul 05 2014 *) CoefficientList[Series[(2 x^12 + x^9 + x^8 + x^7 + x^6 + x^2 + x + 1) / (x^4 - x^3 - x + 1), {x, 0, 100}], x] (* Vincenzo Librandi, Feb 22 2018 *)
Formula
From Chai Wah Wu, Feb 21 2018: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 13.
G.f.: x*(2*x^12 + x^9 + x^8 + x^7 + x^6 + x^2 + x + 1)/(x^4 - x^3 - x + 1). (End)
a(n) = 2*n + 3*floor(n/3 + 2/3) - 17 for n>9. - Bruno Berselli, Feb 22 2018
Comments