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A091990 Number of reduced magic borders of order n (these extend magic squares of order n-2 to order n). 0
1, 2, 10, 140, 185, 28490, 3568, 4117006, 68166, 695025466, 1324149 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,2
COMMENTS
Definition for a magic border: imagine the border of a square matrix: E_1={a_{1,1},...,a_{1,n}} upper, E_2={a_{1,1},...,a_{n,1}} left, E_3={a_{n,1},...,a_{n,n}} lower, E_4={a_{1,n},...,a_{n,n}} right edge. Distribute the pairs of numbers (0,n^2-1),...,(2n-3,n^2-2n+2) (each once) on (a_{1,1},a_{n,n}), (a_{1,n},a_{n,1}) the pairs of corner elements and (a_{1,i},a_{n,i}), (a_{i,1},a_{i,n}) (i=2,...,n-1) the pairs of edges so that for k=1,...,4: sum_{a\in E_k) a = const. Reduced means that the pairs of corners, (a_{1,2},...,a_{1,n-1}) and (a_{2,1},...,a_{n-1,1}) are in ascending order.
REFERENCES
M. Kraitchik, Bordered Squares. Section 7.7 in Mathematical Recreations, Dover, NY, 2nd ed., 1953, pp. 167-170
LINKS
CROSSREFS
Sequence in context: A270589 A171214 A213955 * A014228 A059475 A156296
KEYWORD
more,nonn
AUTHOR
Andreas W. Reinhart (reinhart(AT)castor.uni-trier.de), Mar 17 2004
STATUS
approved

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Last modified March 2 21:56 EST 2024. Contains 370498 sequences. (Running on oeis4.)