A177895 - OEIS

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A177895

Trace of the square matrix whose rows are the cyclic permutations of the digits of n.

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

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+j-1]); trace(m)} \\ David A. Corneth, Jun 13 2017

CROSSREFS

Sequence in context: A344486 A138795 A297233 * A340184 A238986 A227876

Adjacent sequences: A177892 A177893 A177894 * A177896 A177897 A177898

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Dec 15 2010

STATUS

approved