帕斯卡三角形與2的幂

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

1 10 45 120 210 252 210 120 45 10 1

1 11 55 165 330 462 462 330 165 55 11 1

1 12 66 220 495 792 924 792 495 220 66 12 1

1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1

1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1

1 15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1

性質

第n行數字和是2^(n-1)

1 = 1

1+1 = 2

1+2+1 = 4

1+3+3+1 = 8

1+4+6+4+1 = 16

1+5+10+10+5+1 = 32

1+6+15+20+15+6+1 = 64

1+7+21+35+35+21+7+1 = 128

1+8+28+56+70+56+28+8+1 = 256