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Search: id:A035006
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| A035006 |
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Number of possible rook moves on an n X n chessboard. |
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+0
4
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| 0, 8, 36, 96, 200, 360, 588, 896, 1296, 1800, 2420, 3168, 4056, 5096, 6300, 7680, 9248, 11016, 12996, 15200, 17640, 20328, 23276, 26496, 30000, 33800, 37908, 42336, 47096, 52200, 57660, 63488, 69696, 76296, 83300, 90720, 98568, 106856
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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E. Bonsdorff, K. Fabel and O. Riihimaa, Schach und Zahl (Chess and numbers), Walter Rau Verlag, Dusseldorf, 1966.
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FORMULA
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a(n)=(n-1)*2*n^2
sum (((n+j-1)^2-(n-j+1)^2),j=1..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 13 2006
1/A035006[n+1]=int(x*h(x),x=1/(n+1)..1/n)=int(x*(1/x-floor(1/x)),x=1/(n+1)..1/n)=1/((2*(n^2+2*n+1))*n) and sum(1/((2*(n^2+2*n+1))*n),n=1..infinity)=1-Zeta(2)/2 where h(x) is the Gauss (continued fraction) map h(x)={x^-1} and {x} is the fractional part of x [From Stephen Crowley (crow(AT)crowlogic.net), Jul 24 2009]
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EXAMPLE
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On a 3 X 3-board, rook has 9*4 moves, so a(3)=36.
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CROSSREFS
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Cf. A033586, A035006-A035008.
Sequence in context: A048740 A139608 A009923 this_sequence A032768 A006636 A092365
Adjacent sequences: A035003 A035004 A035005 this_sequence A035007 A035008 A035009
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com)
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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