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anemone
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Consider the triangular array of numbers \(\displaystyle 0,\;1,\;2,\;3,\cdots\) along the sides and interior numbers obtained by adding the two adjacent numbers in the previoius row. Row 1 through row 6 are shown as below.
Let \(\displaystyle f(n)\) denote the sum of the numbers in row \(\displaystyle n\). What is the remainder when \(\displaystyle f(100)\) is divided by \(\displaystyle 100\)?
0 | ||||||||||
1 | 1 | |||||||||
2 | 2 | 2 | ||||||||
3 | 4 | 4 | 3 | |||||||
4 | 7 | 8 | 7 | 4 | ||||||
5 | 11 | 15 | 15 | 11 | 5 |
Let \(\displaystyle f(n)\) denote the sum of the numbers in row \(\displaystyle n\). What is the remainder when \(\displaystyle f(100)\) is divided by \(\displaystyle 100\)?