That gives 5*13/14 * 210240 = 976114 new coins per year. Annual decline yields infinite geometric serie and we got approx 976114 * 1/(1-13/14) = 13.6kk additional coins. Add the current supply = 6kk and that result in ~20kk total coins.
What did I miss?
Ignoring the first 5464 blocks where the rewards were computed differently (would adds roughly 2.7 million coins in the worst case):
5*210240
5*13/14*210240
5*13/14*13/14*210240
5*13/14*13/14*13/14*210240
...
I've just thrown the formula above into a little shell script for the next 36 years (because 2050 was mentioned):
Computing mined coins for 36 years:
Year: 2014, New coins: 1051200, Sum: 1051200)
Year: 2015, New coins: 976114, Sum: 2027314)
Year: 2016, New coins: 906391, Sum: 2933706)
Year: 2017, New coins: 841649, Sum: 3775355)
Year: 2018, New coins: 781531, Sum: 4556887)
Year: 2019, New coins: 725708, Sum: 5282595)
Year: 2020, New coins: 673871, Sum: 5956467)
Year: 2021, New coins: 625738, Sum: 6582205)
Year: 2022, New coins: 581042, Sum: 7163247)
Year: 2023, New coins: 539539, Sum: 7702787)
Year: 2024, New coins: 501000, Sum: 8203788)
Year: 2025, New coins: 465215, Sum: 8669003)
Year: 2026, New coins: 431985, Sum: 9100988)
Year: 2027, New coins: 401129, Sum: 9502118)
Year: 2028, New coins: 372477, Sum: 9874595)
Year: 2029, New coins: 345871, Sum: 10220467)
Year: 2030, New coins: 321166, Sum: 10541633)
Year: 2031, New coins: 298226, Sum: 10839859)
Year: 2032, New coins: 276924, Sum: 11116784)
Year: 2033, New coins: 257143, Sum: 11373928)
Year: 2034, New coins: 238776, Sum: 11612704)
Year: 2035, New coins: 221721, Sum: 11834425)
Year: 2036, New coins: 205883, Sum: 12040309)
Year: 2037, New coins: 191177, Sum: 12231487)
Year: 2038, New coins: 177522, Sum: 12409009)
Year: 2039, New coins: 164842, Sum: 12573852)
Year: 2040, New coins: 153067, Sum: 12726919)
Year: 2041, New coins: 142134, Sum: 12869054)
Year: 2042, New coins: 131981, Sum: 13001035)
Year: 2043, New coins: 122554, Sum: 13123590)
Year: 2044, New coins: 113800, Sum: 13237391)
Year: 2045, New coins: 105672, Sum: 13343063)
Year: 2046, New coins: 98124, Sum: 13441187)
Year: 2047, New coins: 91115, Sum: 13532302)
Year: 2048, New coins: 84606, Sum: 13616909)
Year: 2049, New coins: 78563, Sum: 13695473)
Year: 2050, New coins: 72951, Sum: 13768424)
Easy to see that the lower limit is about 14 million coins, add to that the (worst case) 2.7 millions and you'd have about 16.6 million expected coins.
No idea why ~22 millions are mentioned in the source code, maybe Evan assumed some average difficulty back then.
But, to be honest, I don't really care. 2 postings here per week are more than enough.