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A026475 a(1)=1, a(2)=3, otherwise a(n) = least positive integer > a(n-1) and not a(i) + a(j) + a(k) for 1 <= i < j < k <= n.

%I A026475 #23 Mar 07 2025 01:29:44
%S A026475 1,3,4,5,6,7,19,20,21,22,36,37,38,39,53,54,55,69,70,71,72,86,87,88,
%T A026475 102,103,104,105,119,120,121,135,136,137,138,152,153,154,168,169,170,
%U A026475 171,185,186,187,201,202,203,204,218,219,220,234,235,236,237,251,252,253
%N A026475 a(1)=1, a(2)=3, otherwise a(n) = least positive integer > a(n-1) and not a(i) + a(j) + a(k) for 1 <= i < j < k <= n.
%C A026475 Without specifying a(2)=3, a(2) would be 2 and sequence would be A026471. - _Robert Israel_, Aug 27 2018
%H A026475 Robert Israel, <a href="/A026475/b026475.txt">Table of n, a(n) for n = 1..10000</a>
%H A026475 Wieb Bosma, Rene Bruin, Robbert Fokkink, Jonathan Grube, Anniek Reuijl, and Thian Tromp, <a href="https://arxiv.org/abs/2503.04122">Using Walnut to solve problems from the OEIS</a>, arXiv:2503.04122 [math.NT], 2025.
%H A026475 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A026475 a(n+7) = a(n) + 33 for n >= 8. - _Robert Israel_, Aug 27 2018
%F A026475 From _Colin Barker_, Oct 10 2019: (Start)
%F A026475 G.f.: x*(1 + 2*x + x^2 + x^3 + x^4 + x^5 + 12*x^6 - x^8 + 13*x^10 - 11*x^13 + 13*x^14) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).
%F A026475 a(n) = a(n-1) + a(n-7) - a(n-8) for n>15.
%F A026475 (End)
%p A026475 1, 3, 4, 5, 6, 7, 19, seq(op([20, 21, 22, 36, 37, 38, 39]+k*[33$7]),k=0..10); # _Robert Israel_, Aug 30 2018
%t A026475 LinearRecurrence[{1,0,0,0,0,0,1,-1},{1,3,4,5,6,7,19,20,21,22,36,37,38,39,53},60] (* _Harvey P. Dale_, Jan 04 2022 *)
%o A026475 (PARI) Vec(x*(1 + 2*x + x^2 + x^3 + x^4 + x^5 + 12*x^6 - x^8 + 13*x^10 - 11*x^13 + 13*x^14) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^40)) \\ _Colin Barker_, Oct 10 2019
%Y A026475 Cf. A026471.
%K A026475 nonn,easy
%O A026475 1,2
%A A026475 _Clark Kimberling_
%E A026475 More terms from Larry Reeves (larryr(AT)acm.org), Sep 25 2000