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 Concerning combinatorics (Posted on 2011-10-04)
Take a row of Pascals Triangle. Write a second copy of the row below it but with an offset. Multiply each pair of numbers and then sum these products. (A missing number is considered to be zero.)

The result is number further down the Triangle.

Can you explain or prove the result?

Example with the 4th row and offset by 1:

```1    4    6    4    1    0
0    1    4    6    4    1
0 +  4 + 24 + 24 +  4 +  0 = 56 which is in row 8.```

 No Solution Yet Submitted by Jer Rating: 4.5000 (2 votes)

 Subject Author Date re: 1 step further. Not commutative. Bractals 2011-10-07 07:30:00 1 step further Steve Herman 2011-10-06 00:45:18 1 step further. Jer 2011-10-05 10:53:14 re: Happy 35th anniversary (spoiler) -my way Ady TZIDON 2011-10-05 10:01:33 Happy 35th anniversary (spoiler) Steve Herman 2011-10-04 23:55:12 Result explaned - No Proof Bractals 2011-10-04 12:56:56 Possible explanation broll 2011-10-04 12:53:20

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