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A035006
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Number of possible rook moves on an n X n chessboard.
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9
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Obviously A035005(n) = A002492(n-1) + A035006(n) since Queen = Bishop + Rook. [From Johannes W. Meijer (meijgia(AT)hotmail.com), Feb 04 2010.]
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REFERENCES
| E. Bonsdorff, K. Fabel and O. Riihimaa, Schach und Zahl (Chess and numbers), Walter Rau Verlag, Dusseldorf, 1966.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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FORMULA
| 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]
a(n) = 4 * A006002(n-1). [From Johannes W. Meijer, Feb 04 2010]
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EXAMPLE
| On a 3 X 3-board, rook has 9*4 moves, so a(3)=36.
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PROG
| (MAGMA) [(n-1)*2*n^2: n in [1..40]]; // Vincenzo Librandi, Jun 16 2011
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CROSSREFS
| Cf. A033586 (King), A035005 (Queen), A035008 (Knight), A002492 (Bishop) and A049450 (Pawn).
Sequence in context: A139608 A009923 A187287 * A032768 A006636 A092365
Adjacent sequences: A035003 A035004 A035005 * A035007 A035008 A035009
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Ulrich Schimke (ulrschimke(AT)aol.com)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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