A333675 Partial sums of non-Lucas numbers A057854.

5, 11, 19, 28, 38, 50, 63, 77, 92, 108, 125, 144, 164, 185, 207, 230, 254, 279, 305, 332, 360, 390, 421, 453, 486, 520, 555, 591, 628, 666, 705, 745, 786, 828, 871, 915, 960, 1006, 1054, 1103, 1153, 1204, 1256, 1309, 1363, 1418, 1474, 1531, 1589, 1648, 1708, 1769

Offset: 1

Author

Daniel Hoyt, Apr 01 2020

Keywords

• easy
• nonn
• hear

Links

• Daniel Hoyt, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A138105, A057854, A000032.

Programs

Mathematica

a[n_] := With[{phi = (1 + Sqrt[5])/2}, Floor[1/2 - LambertW[-1, -Log[phi]/phi^(n + 1/2)]/Log[phi]]];
Accumulate[Table[a[n], {n, 1, 60}]]

Python

N = 60
notlucas = []
lucas = [2, 1]
for x in range(N):
    a = lucas[x] + lucas[x+1]
    lucas.append(a)
notlucas = [x for x in range(1, len(lucas)) if x not in lucas]
A333675 = []
for y in range(len(notlucas)):
    a = sum(notlucas[:y]) + notlucas[y]
    A333675.append(a)
print(', '.join(str(x) for x in A333675))