Reward schedule and maximum number of dogecoins? According to Dogecoin's bitcointalk-thread there will be a maximum of 100 billion dogecoins. Yet, just below that figure is stated that the reward schedule offers a reward of up to 1 million dogecoins for each of the first 100k block, which would amount to 100,000,000,000 doges already rewarded for the first 100,000 blocks. The subsequent next 500k blocks would up the total doges to just shy of 170 billion dogecoins.

It also states that there will be a constant reward of 10k doges starting with block 600,001.

This information is inconsistent and I am wondering, how the reward schedule is actually implemented:
Is there a maximum of dogecoins or will the amount continue to grow infinitely as suggested by the constant reward?
The Dogecoin reward schedule
I subsequently found the information that the Dogecoin reward schedule provides random amounts sized between 0 and a halving maximum for the first 600,000 blocks:

Block 1 — 100,000: 0-1,000,000 dogecoins
Block 100,001 — 200,000: 0-500,000 dogecoins
Block 200,001 — 300,000: 0-250,000 dogecoins
Block 300,001 — 400,000: 0-125,000 dogecoins
Block 400,001 — 500,000: 0-62,500 dogecoins
Block 500,001 — 600,000: 0-31,250 dogecoins
Block 600,001+: 10,000 dogecoins

The random reward amounts are dependent on the hash of the previous block. (H/T @JesseBusman)
How much?
At optimal random distribution, the first reward interval would provide 50 billion dogecoins. Altogether, the first 600,000 blocks would provide an estimated ~98.44 billion dogecoins, leaving another expected 156,250 blocks to be mined with the subsequent constant block reward of 10,000 doges per block.
How long?
As the block time is aimed to be 60 seconds, the reward is expected to halve every 69 days, 10 hours and forty minutes. At optimal block time, the last block with a reward would be expected after 525 days, or one year and 160 days.
Update: Flat 10k reward forever
On February 1st, 2014 the Dogecoin developers announced that Dogecoin would not be capped at 100 billion dogecoins after all, but would continue to have a flat 10k dogecoin reward for each block after Block 600,000.
While not hard-capped, a constant tail emission is predictable and disinflationary: