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A242513
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a(n) = maximal number of shortest knight's move paths, from origin at center of an infinite open chessboard, to any square within n moves.
(history;
published version)
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#33 by N. J. A. Sloane at Fri May 23 23:07:48 EDT 2014
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#32 by N. J. A. Sloane at Fri May 23 23:07:45 EDT 2014
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#31 by N. J. A. Sloane at Fri May 23 00:37:29 EDT 2014
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#30 by Jon E. Schoenfield at Thu May 22 23:52:16 EDT 2014
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#29 by Jon E. Schoenfield at Thu May 22 23:52:13 EDT 2014
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| NAME
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a(n) = maximal number of shortest knight's move paths, from origin at center of an infinite open chess boardchessboard, to any square within n moves.
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| STATUS
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approved
editing
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#28 by N. J. A. Sloane at Wed May 21 20:31:54 EDT 2014
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#27 by Michel Marcus at Wed May 21 13:18:02 EDT 2014
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Discussion
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Wed May 21
| 20:41
| Jon E. Schoenfield: Joerg -- I could be mistaken on this (even though I'm a native speaker of American English, and I think I do okay at writing it, most of the time <g>), but here's how I see it:
Constructions like
A is replaced by B
or
A was replaced by B
are okay if B is the entity doing the replacing. (The passive voice is used in both of the above examples, and those who urge that active voice be used wherever possible would prefer
B replaces A
or
B replaced A
... but I'm not bothered by the use of passive voice. [Or should I say "the use of passive voice does not bother me"?]) ;-)
However, when there's a third entity doing the replacing, I think it's a different situation. If an explicit reference is made to that third entity, e.g., in
I replaced A ___ B
or
He should replace A ___ B
... I can't remember ever having seen "by" used in the blank; I've seen only the word "with" used in constructions like those.
Now, it's true that the sentence at hand in the Comments section doesn't explicitly refer to an entity that's doing the replacing. But (and, again, I could be mistaken) I think the same rule applies, and
The same sequence results after replacing A with B.
seems correct to me, while
The same sequence results after replacing A by B.
seems incorrect.
Perhaps complicating the situation is the fact that what I conveniently replaced above with the letter A is a phrase that includes the word "within" ... and it may be that the presence of that word so close to 'with' makes
replacing 'within n moves' with
seem a little awkward.
Anyway, that's the way I see it, but if you and/or others see it differently, I won't complain if you decide to replace my "with" _with_ "by" ... ;-)
Thanks for your time in reading this blathering pink-box comment! -- Jon
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#26 by Michel Marcus at Wed May 21 13:17:52 EDT 2014
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| EXAMPLE
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For n=5, there are 100 shortest paths of length 5 steps from (0,0) to (7,0);); no square at 5 (or fewer) moves from the origin has more shortest paths.
no square at 5 (or fewer) moves from the origin has more shortest paths.
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| KEYWORD
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easy,nonn,more,walk,new
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| STATUS
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proposed
editing
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Discussion
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Wed May 21
| 13:18
| Michel Marcus: I think more keyword not needed any longer.
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#25 by Jon E. Schoenfield at Mon May 19 22:11:32 EDT 2014
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Discussion
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Tue May 20
| 03:16
| Joerg Arndt: "replace by" looks neater to me (non-native) than "replace with".
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#24 by Jon E. Schoenfield at Mon May 19 22:11:30 EDT 2014
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| COMMENTS
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The same sequence results after replacing ` 'within n moves' by `with 'at shortest distance n moves'.
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| STATUS
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proposed
editing
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