

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
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OFFSET

0,3


LINKS

Table of n, a(n) for n=0..147.


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+j1]); 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



