S
My series is not in there - I looked. I didn't tell
you because I didn't want to spoil the fun :-)
Dishes - eat food, give plate to dog, dog licks
plate clean, problem solved! According to Mythbusters, there are less
bacteria in a dog's mouth than a human's (well Adam's, anyway) so I'm probably
better off diluting my saliva with my dog's. It's one of those things where if
you do it without thinking about it, it works out fine ;-)
0, 1, 3, 6, 10, 16, 24, 34, 46, 60, 76, 94, 114, 137, 163,
...
It is completely valid to specify a starting term (or more). The Fibonacci series itself has the starting terms of either "0, 1" or "1, 1" even though it can be extended "left" by running the rule backwards. If you use "1, 2" and apply the same rule you still get the Fib. series and if you use "0, n" you get a multiple of the series; but if you use "1, 3" (or "1, 4", etc) you get something different.
It is completely valid to specify a starting term (or more). The Fibonacci series itself has the starting terms of either "0, 1" or "1, 1" even though it can be extended "left" by running the rule backwards. If you use "1, 2" and apply the same rule you still get the Fib. series and if you use "0, n" you get a multiple of the series; but if you use "1, 3" (or "1, 4", etc) you get something different.
Your series is interesting. It starts off
regular, then seems to jump to 1 more than the expected value, settles down
again, and then does the +1 trick again! I must admit I am perplexed
:-\
* :-) A light bulb has just appeared above my
head - Start with '0', add '1'. Then add '2' to the next term, then '3', and so
on. This gives 0, (+1)=1, (+2)=3, (+3)=6, (+4)=10.
When the term becomes a double digit number add
whatever number you were going to ('5') plus another '1'. Now increment both of
the numbers to be added by one (+6+2, +7+3, +8+4,...). This gives 10 (+5+1)=16,
(+6+2)=24, (+7+3)=34,...94 (+12+8)=114.
When you hit triple digits add another
'1' into the mix (+13+9+1) and increment all 3 by '1'.
Thus: For a(n) < 10, a(n) = a(n-1) + n; For
10 <= a(n) < 100, a(n) = a(n-1) + n + (n-4);
For 100 <= a(n) < 1000, a(n) = a(n-1) + n
+ (n-4) + (n-8).
This gives (starting with '0') - 0, 1, 3, 6,
10, 16, 24, 34, 46, 60, 76, 94, 114, 137, 163, 192, 224, 259, 297,
338,...
Is that it?
Speaking of not not sleeping, it's nearly 1am -
I'm off to nigh'-nigh's.
M