How much time will I need to unlock my Android phone?
Rebmu: 197 175 168 167 characters

Generates combinations as a series of numbers (ex. 12369 is top-left to top-right to bottom-right), checks if combination is valid, and increments a counter if it is. This might take a while* to run. Returns the number of seconds needed to unlock the phone.

B[[2 13][4 17][6 39][8 79][5 19][5 28][5 37][5 46][a 0]]Fdz[Q1feCb[st[a]paStsC/1 Qa^Qa^e?NNfiAtsC/2 e?NNfiArvTSc/2]]rpJ987653088[StsADj1233iA^e?SuqSf[++K]]adKmp30dvK 5


Unmushed and commented:

; for each subarray c: 
; the sequences c/2 and c/3 are invalid before the point c/1 is pressed
; a 0 - a is never in the sequence, therefore 0 is always invalid
b: [[2 13] [4 17] [6 39] [8 79] [5 19] [5 28] [5 37] [5 46] [a 0]]
; checks (most) conditions of validity
f: dz[
    ; set q to 1
    q: 1
    ; foreach array in b as c
    fe c b [
        ; set a to be portion of s before c/1
        st [a] pa s ts c/1
        ; q = q and (a does not contain c/2) and (a does not contain reverse of c/2)
        q: a^ q 
           a^ e? nn fi a ts c/2 
              e? nn fi a ts rv c/2
    ]
]
; repeat 98765308 times, with j = 1 to 98765308
; 987653088 = 987654321 (largest valid combination) - 1234 (smallest valid combination) + 1
rp j 987653088 [
    ; set s to j+1233 (smallest valid combination - 1) as a string
    s: ts ad j 1233 
    ; if f returns trues and s does not contain duplicates, increment k
    i a^ e? s uq s 
          f
     [++ k]
]
; print k (number of combinations) + 30 * (k/5) -&gt; number of seconds needed
ad k mp 30 dv k 5


The program loops from 1 to (987654321-1233), checking 1233+loop counter (therefore checking 1234 to 987654321). 

If the number 987653088 is replaced with, 9876-1233 or 8643, then the program will find the time taken for all 4-point combinations. 

Output for 9876-1233=8643 (4-point combinations):

&gt;&gt; rebmu %combinations.rebmu
== 11344


Output for 98765-1233=97532 (4 and 5-point combinations):

&gt;&gt; rebmu %combinations.rebmu
== 61426


Output for 987654-1233=986421 (4,5,6-point combinations):

&gt;&gt; rebmu %combinations.rebmu
== 243532




*4/5-point took me about 8 seconds to run; 4-6 took about 77 seconds. It might take ~24 hours or longer depending on who runs this to calculate number of combinations for 4-9 point combinations.