Kata

John and his wife Ann have decided to go to Codewars. On the first day Ann will do one kata and John - he wants to know how it is working - 0 kata.

Let us call a(n) - and j(n) - the number of katas done by Ann - and John - at day n. We have a(0) = 1 and in the same manner j(0) = 0.

They have chosen the following rules:

• On day n the number of katas done by Ann should be n minus the number of katas done by John at day t, t being equal to the number of katas done by Ann herself at day n - 1

• On day n the number of katas done by John should be n minus the number of katas done by Ann at day t, t being equal to the number of katas done by John himself at day n - 1

Whoops! I think they need to lay out a little clearer exactly what there're getting themselves into!

Could you write:

• functions ann(n) and john(n) that return the list of the number of katas Ann/John does on the first n days;
• functions sum_ann(n) and sum_john(n) that return the total number of katas done by Ann/John on the first n days

Examples:

john(11)  -->  [0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6]
ann(6)    -->  [1, 1, 2, 2, 3, 3]

sum_john(75)  -->  1720
sum_ann(150)  -->  6930

Note:

Keep an eye on performance.