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
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
KEYWORD
easy,nice,nonn
AUTHOR
Graziano Aglietti (mg5055(AT)mclink.it), Sep 02 2010
STATUS
approved