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%I #19 Mar 14 2020 13:02:13
%S 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,
%T 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,
%U 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
%N Trace of the square matrix whose rows are the cyclic permutations of the digits of n.
%F For n=a, trace(M) = a;
%F for n=ab, trace(M) = 2a;
%F for n=abc, trace(M) = a + b + c;
%F for n=abcd, trace(M) = 2a + 2c.
%e a(123) = 6, because M =
%e [1 2 3]
%e [2 3 1]
%e [3 1 2]
%e and trace(M) = 6.
%o (Sage)
%o def A177895(n):
%o d = n.digits()[::-1] if n > 0 else [0]
%o M = Matrix(lambda i,j: d[(i+j) % len(d)], nrows=len(d))
%o return M.trace() # _D. S. McNeil_, Dec 16 2010
%o (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
%K nonn,base
%O 0,3
%A _Michel Lagneau_, Dec 15 2010