A177895 - OEIS

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A177895

Trace of the square matrix whose the 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]`
	CROSSREFS	`Sequence in context: A061816 A083960 A138795 * A189506 A173529 A093017` `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 May 22 16:23 EDT 2013. Contains 225553 sequences.