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Let B(n) denote the number of distinct norms <=n in the square lattice and let B_3(n) denote the number of distinct norms <=n in the hexagonal lattice; sequence gives B(n) - B3(n).

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0, 1, 0, 0, 1, 1, 0, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 4, 4, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 4, 4, 5, 5, 4, 5, 5, 5, 5, 6, 6, 7, 6, 5, 5, 5, 4, 5, 5, 6, 6, 5, 6, 6, 6, 6, 7, 8, 7, 7, 6, 6, 6, 6, 6, 7, 7 (list; graph; listen)

	OFFSET	`0,10`
	COMMENT	`It was conjectured by Schmutz Schaller that B(x)>=B_3(x) for every x; this was proved in the reference given.`
	REFERENCES	`P. Moree and H. J. J. te Riele, The hexagonal versus the square lattice, Math. Comp. 73 (2004), no. 245, 451-473.`
	LINKS	`P. Moree and H. J. J. te Riele, The hexagonal versus the square lattice`
	MAPLE	`for j from 0 to 200 do; a[j] := 0; b[j] := 0; end do: for i from 0 to 15 do; for j from 0 to 15 do; u := ii+jj; v := ii+3j*j; if u<201 then a[u] := 1; end if; if v<201 then b[v] := 1; end if; end do; end do: u := 0: for j from 0 to 200 do; u := u+a[j]-b[j]; print(j, u); end do:`
	CROSSREFS	`Sequence in context: A073772 A164562 A058188 this_sequence A037803 A030410 A085301` `Adjacent sequences: A069997 A069998 A069999 this_sequence A070001 A070002 A070003`
	KEYWORD	`nonn,nice,easy`
	AUTHOR	`P. Moree (moree(AT)science.uva.nl), May 03 2002`

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Last modified November 25 14:49 EST 2009. Contains 167514 sequences.

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