The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13...; starting with 0 and 1, each number is the sum of the two previous numbers.
The Lucas numbers follow the same rule, but start with 2 and 1: 2, 1, 3, 4, 7, 11, 18,...
What's the sum of the first k Lucas numbers?
What's the sum of the squares of the first k Lucas numbers?
For comparison with formulae:
n L(n) Sum(L(n)) Sum((L(n))^2)
1 2 2 4
2 1 3 5
3 3 6 14
4 4 10 30
5 7 17 79
6 11 28 200
7 18 46 524
8 29 75 1365
9 47 122 3574
10 76 198 9350
11 123 321 24479
12 199 520 64080
13 322 842 167764
14 521 1363 439205
15 843 2206 1149854
16 1364 3570 3010350
17 2207 5777 7881199
18 3571 9348 20633240
19 5778 15126 54018524
20 9349 24475 141422325
21 15127 39602 370248454
22 24476 64078 969323030
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Posted by Charlie
on 2004-10-07 13:11:42 |
some numbers
