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%I #17 Jun 29 2023 18:52:11
%S 1,2,3,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91,97,103,109,115,121,
%T 127,133,139,145,151,157,163,169,175,181,187,193,199,205,211,217,223,
%U 229,235,241,247,253,259,265,271,277,283,289,295,301,307,313,319,325
%N a(1) = 1, a(2) = 2, a(3) = 3, a(n) = least number not the sum of three or fewer previous terms.
%C Generalization: let the first k terms of the sequence be 1,2,...,k, and for n > k, let b(n) be defined as the least positive integer that is not the sum of k or fewer previous terms; then b(n+k) = b(n) + n* k(k+1)/2. b(n) = (n+1)*k*(k+1)/2 + 1. n > k. Here a(n) is for k=3.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F a(n+4) = a(4) + 6n for n > 4; a(n) = 6n - 17, n >3.
%F From _Chai Wah Wu_, Oct 25 2018: (Start)
%F a(n) = 2*a(n-1) - a(n-2) for n > 5.
%F G.f.: x*(2*x^4 + 3*x^3 + 1)/(x - 1)^2. (End)
%t a[1] = 1; a[2] = 2; a[3] = 3; a[n_] := a[n] = (m = 1; l = n - 1; t = Union[ Flatten[ Join[ Table[ a[i], {i, l}], Table[ a[i] + a[j], {i, l}, {j, i + 1, l}], Table[ a[i] + a[j] + a[k], {i, l}, {j, i + 1, l}, {k, j + 1, l}] ]]]; While[ Position[t, m] != {}, m++ ]; m); Table[ a[n], {n, 60}] (* _Robert G. Wilson v_, Dec 14 2004 *)
%Y Essentially the same as A016921.
%K easy,nonn
%O 1,2
%A _Amarnath Murthy_, Nov 25 2004
%E More terms from _Robert G. Wilson v_, Dec 14 2004
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