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A magic triangle or perimeter magic triangle [1] is an arrangement of the integers from 1 to n on the sides of a triangle with the same number of integers on each side, called the order of the triangle, so that the sum of integers on each side is a constant, the magic sum of the triangle.
A bijection with the sums to n is to replace 1 with 0 and 2 with 11. The number of binary strings of length n without an even number of consecutive 0 s or 1 s is 2F n. For example, out of the 16 binary strings of length 4, there are 2F 4 = 6 without an even number of consecutive 0 s or 1 s—they are 0001, 0111, 0101, 1000, 1010, 1110. There is ...
Simply put, each number equals a triangular number plus 1. These are the first number on each row of Floyd's triangle. The lazy caterer's sequence (green) and other OEIS sequences in Bernoulli's triangle. As the third column of Bernoulli's triangle (k = 2) is a triangular number plus one, it forms the lazy caterer's sequence for n cuts, where n ...
Today's Connections Game Answers for Monday, September 11, 2023: 1. TV SHOWS: 24, BONES, FIREFLY, WEEDS 2. HALLOWEEN DECORATIONS: BAT, COBWEB, PUMPKIN, TOMBSTONE 3 ...
1. Something you might hear 2. Certain type of beverage 3. Parts of a certain object 4. Related to gossip. Related: 300 Trivia Questions and Answers to Jumpstart Your Fun Game Night. Ready for the ...
In the case of the lazy caterer's sequence, the maximum number of pieces you can cut a pancake into with n cuts, the OEIS gives the sequence as 1, 2, 4, 7, 11, 16, 22, 29, 37, ... A000124, with offset 0, while Mathworld gives the sequence as 2, 4, 7, 11, 16, 22, 29, 37, ... (implied offset 1).
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1 is read off as "one 1" or 11. 11 is read off as "two 1s" or 21. 21 is read off as "one 2, one 1" or 1211. 1211 is read off as "one 1, one 2, two 1s" or 111221. 111221 is read off as "three 1s, two 2s, one 1" or 312211. The look-and-say sequence was analyzed by John Conway [1] after he was introduced to it by one of his students at a party. [2 ...