WON plate88 | World!OfNumbers Counting palindromic patterns [ January 13, 2001 ] Marks R. Nester from Australia investigated thoroughly palindromic structures and made various integer sequences resulting from the count. I felt that this topic is so basic for my palindrome website that it should have appeared much earlier... but 'better late than never' the saying goes. (Source: see Sloane's integer sequences A056449 up to A056523) The description of, for instance A056450, is as follows Palindromes using a maximum of four different characters. The "palindromicy" refers to the number of palindromes that one can make using an alphabet of four letters. Suppose a, b, c, d are the only letters in our alphabet. Then for words of length 1 the only (trivial) palindromes are the letters themselves, i.e. a, b, c, d. (4 altogether) For words of length 2 the only palindromes are: aa, bb, cc, dd. (4 altogether) For words of length 3 the only palindromes are: aaa, aba, aca, ada, bab, bbb, bcb, bdb, cac, cbc, ccc, cdc, dad, dbd, dcd, ddd. (16 altogether) etc... Proceeding in this fashion we obtain the sequence 4, 4, 16, ... A000088 Prime Curios! Prime Puzzle Wikipedia 88 Le Nombre 88 Numberland 88
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