This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365907 #25 Oct 19 2023 23:15:22
%S A365907 0,1,5,16,63,262,1105,4676,19803,83882,355325,1505176,6376023,
%T A365907 27009262,114413065,484661516,2053059123,8696898002,36840651125,
%U A365907 156059502496,661078661103,2800374146902,11862575248705,50250675141716,212865275815563,901711778403962
%N A365907 Smallest nonnegative integer that is not the sum of fewer than n signed Lucas numbers.
%C A365907 Signed Lucas numbers are the union of A000032 and A061084.
%H A365907 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-3,-1).
%F A365907 a(n) = n, for n<2.
%F A365907 a(n) = (A000032(3*n-2)+3)/2 = 1+4+Sum_{i=2..n-1} A000032(3*n-1), for n>1.
%F A365907 G.f.: x*(1 - 6*x^2 - x^3)/((1 - x)*(1 - 4*x - x^2)). - _Stefano Spezia_, Sep 25 2023
%e A365907 a(0) = 0, the sum of 0 Lucas numbers.
%e A365907 a(1) = 1 = A000032(1), the sum of 1 Lucas number.
%e A365907 a(2) = 5 = 1+4 = A000032(1)+A000032(3), the sum of 2 Lucas numbers. (2, 3, and 4 need only one term, since they are Lucas numbers.)
%e A365907 a(4) = 63 = 1+4+11+47.
%e A365907 For comparison, 45 is the first sum requiring 4 positive Lucas numbers (45 = 1+4+11+29, see A004146), but here 45 = 47+2-4 requires only 3 signed Lucas numbers so that a(4) != 45.
%t A365907 LinearRecurrence[{5, -3, -1}, {0, 1, 5, 16, 63}, 26] (* _Amiram Eldar_, Sep 26 2023 *)
%o A365907 (Python)
%o A365907 from sympy import lucas
%o A365907 a = lambda n: n if n<2 else (lucas(3*n-2)+3)//2
%Y A365907 Cf. A000032, A061084, A004146 (analogous with only positive Lucas numbers).
%K A365907 nonn,easy
%O A365907 0,3
%A A365907 _Mike Speciner_, Sep 22 2023