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On the Numbers of Palindromes
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  • Journal title : Kyungpook mathematical journal
  • Volume 56, Issue 2,  2016, pp.349-355
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2016.56.2.349
 Title & Authors
On the Numbers of Palindromes
Bang, Sejeong; Feng, Yan-Quan; Lee, Jaeun;
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For any integer , each palindrome of n induces a circulant graph of order n. It is known that for each integer , there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. [2]). This bijection gives a one-to-one correspondence of the palindromes with to the connected circulant graphs. It was also shown that the number of palindromes of n with is the same number of aperiodic palindromes of n. Let (resp. ) be the number of aperiodic palindromes of n with (resp. ). Let (resp. ) be the number of periodic palindromes of n with (resp. ). In this paper, we calculate the numbers , , , in two ways. In Theorem 2.3, we recurrence relations for , , , in terms of for and . Afterwards, we nd formulae for , , , explicitly in Theorem 2.5.
compositions of n;palindromes;circulant graphs;
 Cited by
H. Baek, The number of aperiodic palindromes of n ${\leq}$ 127, available at

H. Baek. S. Bang, D. Kim and J. Lee, A bijection between aperiodic palindromes and connected circulant graphs, preprint.

S. Heuhach, P. Chinn and R. Grimaldi, Rises, Levels, Drops and "+" Signs in Compositions: Extensions of a Paper by Alladi and Hoggatt, Fibonacci Quarterly 41(3)(1975), 229-239.

N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences,