A180413 Total number of possible knight moves on an n X n X n chessboard, if the knight is placed anywhere.

0, 144, 576, 1440, 2880, 5040, 8064, 12096, 17280, 23760, 31680, 41184, 52416, 65520, 80640, 97920, 117504, 139536, 164160, 191520, 221760, 255024, 291456, 331200, 374400, 421200, 471744, 526176, 584640, 647280, 714240, 785664, 861696

Offset

1,2

Comments

The maximum number of move in tridimensional chessboard is 24, 8 for every dimension. In a vertex the number is smaller.

Binomial transform of [144, 432, 432, 144, 0, 0, 0, ...] = (144, 576, 1440, ...). - Gary W. Adamson, Sep 03 2010

Links

Table of n, a(n) for n=1..33.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 24*n*(n^2-1).

G.f.: 144*x^2/(1-x)^4. - Colin Barker, Mar 17 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=0, a(2)=144, a(3)=576, a(4)=1440. - Harvey P. Dale, Feb 13 2013

E.g.f.: 24 * exp(x) * x^2 * (3 + x). - Vaclav Kotesovec, Feb 15 2015

Mathematica

Table[24n(n^2-1), {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 144, 576, 1440}, 40] (* Harvey P. Dale, Feb 13 2013 *)

Prog

(PARI) a(n)=24*n*(n^2-1) \\ Charles R Greathouse IV, Nov 03 2014

Crossrefs

Cf. A027480, A135503, A180319, A035008.

Sequence in context: A017402 A155707 A017522 * A137885 A204398 A204391

Adjacent sequences: A180410 A180411 A180412 * A180414 A180415 A180416

Keyword

easy,nice,nonn

Author

Graziano Aglietti (mg5055(AT)mclink.it), Sep 02 2010

Status

approved