A244151 0-additive sequence: start with a(1) = 2; thereafter, a(n) = smallest number not already in sequence which is not the sum of any previous two terms.
2, 3, 4, 8, 9, 14, 15, 20, 21, 26, 27, 32, 33, 38, 39, 44, 45, 50, 51, 56, 57, 62, 63, 68, 69, 74, 75, 80, 81, 86, 87, 92, 93, 98, 99, 104, 105, 110, 111, 116, 117, 122, 123, 128, 129, 134, 135, 140, 141, 146, 147, 152, 153, 158, 159, 164, 165, 170, 171, 176, 177, 182, 183, 188, 189, 194, 195, 200, 201, 206, 207, 212, 213
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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Mathematica
f[s_List] := Block[{k = s[[-1]] + 1, ss = Union[Plus @@@ Subsets[s, {2}]]}, While[ MemberQ[ss, k], k++]; Append[s, k]]; Nest[f, {2}, 70] (* Robert G. Wilson v, Jun 23 2014 *) -
PARI
Vec(x*(x^5+3*x^3-x^2+x+2)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Jun 26 2014
Formula
a(2n) = 6(n-1)+2 & a(2n+1) = 6(n-1)+3 for n>1. - Robert G. Wilson v, Jun 23 2014
From Colin Barker, Jun 26 2014: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 6.
G.f.: x*(x^5 + 3*x^3 - x^2 + x + 2)/((x - 1)^2*(x + 1)). (End)
E.g.f.: (x^3 + 3*x^2 + 30*x + 24)/6 + (3*x - 4)*cosh(x) + 3*(x - 2)*sinh(x). - Stefano Spezia, Apr 15 2023
Extensions
Added terms >= 20, Joerg Arndt, Jun 22 2014
Comments