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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

Table of n, a(n) for n=1..41.

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: A267637 A238648 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 June 16 06:46 EDT 2019. Contains 324145 sequences. (Running on oeis4.)