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 A177895 Trace of the square matrix whose rows are the cyclic permutations of the digits of n. 1
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA For n=a, trace(M) = a; for n=ab, trace(M) = 2a; for n=abc, trace(M) = a + b + c; for n=abcd, trace(M) = 2a + 2c. EXAMPLE a(123) = 6, because M =   [1 2 3]   [2 3 1]   [3 1 2] and trace(M) = 6. PROG (Sage) def A177895(n): ....d = n.digits()[::-1] if n > 0 else [0] ....M = Matrix(lambda i, j: d[(i+j) % len(d)], nrows=len(d)) ....return M.trace() # D. S. McNeil, Dec 16 2010 (PARI) a(n) = {if(n<10, return(n)); my(d = digits(n), m, s); d = concat(d, d); s = #d/2; m = matrix(s, s, i, j, d[i+j-1]); trace(m)} \\ David A. Corneth, Jun 13 2017 CROSSREFS Sequence in context: A083960 A138795 A297233 * A238986 A227876 A276716 Adjacent sequences:  A177892 A177893 A177894 * A177896 A177897 A177898 KEYWORD nonn,base AUTHOR Michel Lagneau, Dec 15 2010 STATUS approved

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)