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
Figure-1: Convolution triangle of base length 2.
1
1 1 1
1 2 3 2 1
1 3 6 7 6 3 1
1 4 10 16 19 16 10 4 1
1 5 15 30 45 51 45 30 15 5 1
1 6 21 50 90 126 141 126 90 50 21 6 1
Figure-2: Convolution triangle of base-length 3.
1
1 1 1 1
1 2 3 4 3 2 1
1 3 6 10 12 12 10 6 3 1
1 4 10 20 31 40 44 40 31 20 10 4 1
1 5 15 35 65 101 135 155 155 135 101 65 35 15 5 1
1 6 21 56 120 216 336 456 546 580 546 456 336 216 120 56 21 6 1
Figure-3: Convolution triangle of base length 4.
1 + 2 + 3 + 4 + 5 + 6 + . . . upto n terms
1 + 3 + 6 + 10 + 15 + 21 + . . . upto n terms
1 + 6 + 19 + 45 + 90 + 161 + . . . upto n terms
1 + 5 + 15 + 35 + 70 + 126 + . . . upto n terms
2 + 7 + 16 + 30 + 50 + 77 + . . . upto n terms
1 + 10 + 45 + 141 + 357 + 784 + . . . upto n terms
2 + 12 + 40 + 101 + 216 + 413 + . . . upto n terms
3 + 16 + 51 + 126 + 266 + 504 + . . . upto n terms
3 + 12 + 31 + 65 + 120 + 203 + . . . upto n terms
3 + 31 + 155 + 546 + 1554 + 3823 + . . . upto n terms
3 + 19 + 68 + 185 + 426 + 875 + . . . upto n terms
2 + 18 + 80 + 255 + 666 + 1520 + . . . upto n terms
2 + 33 + 224 + 1015 + 3612 + 10906 + . . . upto n terms
3 + 36 + 206 + 826 + 2667 + 7420 + . . . upto n terms