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 A180319 Total number of possible standard knight moves on an n X 2n chessboard, if the knight is placed anywhere 1
 0, 8, 52, 128, 236, 376, 548, 752, 988, 1256, 1556, 1888, 2252, 2648, 3076, 3536, 4028, 4552, 5108, 5696, 6316, 6968, 7652, 8368, 9116, 9896, 10708, 11552, 12428, 13336, 14276, 15248, 16252, 17288, 18356, 19456, 20588, 21752, 22948, 24176, 25436 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) counts every possible moves of a standard chess knight placed anywhere. For examples, in usual chessboard 8X8 a knight in a corner has only 2 moves, in a central square it has the maximum number of moves:8. Summing all over the 64 squares we have 336 possible moves. Instead on a chessboard 4x8 the number is reduced: ----------------- |2|3|4|4|4|4|3|2| ----------------- |3|4|6|6|6|6|4|3| ----------------- |3|4|6|6|6|6|4|3| ----------------- |2|3|4|4|4|4|3|2| ----------------- the total number is 128 LINKS FORMULA Conjecture: a(n) = 4*(4-9*n+4*n^2) for n>1. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4. G.f.: 4*x^2*(2+7*x-x^2)/(1-x)^3. [Colin Barker, Mar 11 2012] CROSSREFS Cf. A035008 Sequence in context: A238648 A341626 A215834 * A199706 A302318 A035288 Adjacent sequences:  A180316 A180317 A180318 * A180320 A180321 A180322 KEYWORD easy,nonn AUTHOR Graziano Aglietti (mg5055(AT)mclink.it), Aug 27 2010 STATUS approved

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Last modified January 17 22:33 EST 2022. Contains 350410 sequences. (Running on oeis4.)