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A333675 Partial sums of non-Lucas numbers A057854.

%I A333675 #25 May 22 2020 09:45:59
%S A333675 5,11,19,28,38,50,63,77,92,108,125,144,164,185,207,230,254,279,305,
%T A333675 332,360,390,421,453,486,520,555,591,628,666,705,745,786,828,871,915,
%U A333675 960,1006,1054,1103,1153,1204,1256,1309,1363,1418,1474,1531,1589,1648,1708,1769
%N A333675 Partial sums of non-Lucas numbers A057854.
%H A333675 Daniel Hoyt, <a href="/A333675/b333675.txt">Table of n, a(n) for n = 1..10000</a>
%t A333675 a[n_] := With[{phi = (1 + Sqrt[5])/2}, Floor[1/2 - LambertW[-1, -Log[phi]/phi^(n + 1/2)]/Log[phi]]];
%t A333675 Accumulate[Table[a[n], {n, 1, 60}]]
%o A333675 (Python)
%o A333675 N = 60
%o A333675 notlucas = []
%o A333675 lucas = [2, 1]
%o A333675 for x in range(N):
%o A333675     a = lucas[x] + lucas[x+1]
%o A333675     lucas.append(a)
%o A333675 notlucas = [x for x in range(1, len(lucas)) if x not in lucas]
%o A333675 A333675 = []
%o A333675 for y in range(len(notlucas)):
%o A333675     a = sum(notlucas[:y]) + notlucas[y]
%o A333675     A333675.append(a)
%o A333675 print(', '.join(str(x) for x in A333675))
%Y A333675 Cf. A138105, A057854, A000032.
%K A333675 easy,nonn,hear
%O A333675 1,1
%A A333675 _Daniel Hoyt_, Apr 01 2020