Project Euler 148 Pascal's triangle

I solved this one by looking at pattern. Triangular number fractal??? anyway I just used triangular function. from F(1) to F(7) = n(n+1)/2 F(7^2) = F(7)*F(7) F(7^3) = F(7)*F(7)*F(7) what is if F(7^a-3) ? we know that the power of 7 grater than (7^a)-3 is a so we can find this val v = 7^a/7^(a-1) r = 7^a mod 7^(a-1) and finally got recursive function F(7^a-1) = if (r >0) F(v)*F(7)*F(7) + (v+1) * F(r) else F(v)*F(7)*F(7) and Finally I got answer quickly index : 1 1 index : 2 11 index : 3 111 index : 4 1111 index : 5 11111 index : 6 111111 index : 7 1111111 index : 8 1......1 index : 9 11.....11 index : 10 111....111 index : 11 1111...1111 index : 12 11111..11111 index : 13 111111.111111 index : 14 11111111111111 index : 15 1......1......1 index : 16 11.....11.....11 index : 17 111....111....111 index : 18 1111...1111...1111 index : 19 11111..11111..11111 index : 20 111111.111111.111111 index : 21 111111111111111111111 index : 22 1......1......1......1 index : 23 11.....11.....11.....11 index : 24 111....111....111....111 index : 25 1111...1111...1111...1111 index : 26 11111..11111..11111..11111 index : 27 111111.111111.111111.111111 index : 28 1111111111111111111111111111 index : 29 1......1......1......1......1 index : 30 11.....11.....11.....11.....11 index : 31 111....111....111....111....111 index : 32 1111...1111...1111...1111...1111 index : 33 11111..11111..11111..11111..11111 index : 34 111111.111111.111111.111111.111111 index : 35 11111111111111111111111111111111111 index : 36 1......1......1......1......1......1 index : 37 11.....11.....11.....11.....11.....11 index : 38 111....111....111....111....111....111 index : 39 1111...1111...1111...1111...1111...1111 index : 40 11111..11111..11111..11111..11111..11111 index : 41 111111.111111.111111.111111.111111.111111 index : 42 111111111111111111111111111111111111111111 index : 43 1......1......1......1......1......1......1 index : 44 11.....11.....11.....11.....11.....11.....11 index : 45 111....111....111....111....111....111....111 index : 46 1111...1111...1111...1111...1111...1111...1111 index : 47 11111..11111..11111..11111..11111..11111..11111 index : 48 111111.111111.111111.111111.111111.111111.111111 index : 49 1111111111111111111111111111111111111111111111111 index : 50 1................................................1 index : 51 11...............................................11 index : 52 111..............................................111 index : 53 1111.............................................1111 index : 54 11111............................................11111 index : 55 111111...........................................111111 index : 56 1111111..........................................1111111 index : 57 1......1.........................................1......1 index : 58 11.....11........................................11.....11 index : 59 111....111.......................................111....111 index : 60 1111...1111......................................1111...1111 index : 61 11111..11111.....................................11111..11111 index : 62 111111.111111....................................111111.111111 index : 63 11111111111111...................................11111111111111 index : 64 1......1......1..................................1......1......1 index : 65 11.....11.....11.................................11.....11.....11 index : 66 111....111....111................................111....111....111 index : 67 1111...1111...1111...............................1111...1111...1111 index : 68 11111..11111..11111..............................11111..11111..11111 index : 69 111111.111111.111111.............................111111.111111.111111 index : 70 111111111111111111111............................111111111111111111111