Fibonacci appears again (Posted on 2015-08-21)

| 0  0  1  0  0|
| 0  1  0  1  0|
| 1  0  2  0  1|
| 1  3  0  3  1|
| 4  1  6  1  4|
| 5 10  2 10  5|
|15  7 20  7 15|
|22 35 14 35 22|
...

	Submitted by Jer
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Number the columns and put variables in them (3)(2)(1)(2)(3) a b c b a I will consider only the difference (1-2) since the others work the same where b ≤ a < c and c-b > a-b, (1-2)=c-b next row is a+b a+c 2b a+c a+b (1-2)=a+c-2b next row is 2a+b+c a+3b 2a+2c a+3b 2a+b+c (1-2)=a-3b+2c (1-2) in the problem clearly starts 1,1,2,3... as the Fibonacci sequence does. (c-b)+(a-2b+c)=(a-3b+2c) What I showed above is that each difference is the sum of the previous two differences.