OFFSET
0,2
COMMENTS
For n > 1, the number of straight lines with n points in a 4-dimensional hypercube of with n points on each edge is 4n^3 + 12n^2 + 16n + 8, i.e., A105374(n+1).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: 8*x*(1 + x + x^2)/(1-x)^4. - Colin Barker, May 24 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 26 2012
a(n) = 8* A006003(n). - Bruce J. Nicholson, Apr 18 2017
EXAMPLE
a(5) = 4*5^3 + 4*5 = 500 + 20 = 520.
MATHEMATICA
CoefficientList[Series[8*x*(1+x+x^2)/(1-x)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 8, 40, 120}, 50] (* Vincenzo Librandi, Jun 26 2012 *)
PROG
(Magma) I:=[0, 8, 40, 120]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..45]]; // Vincenzo Librandi, Jun 26 2012
(PARI) a(n)=4*n^3+4*n \\ Charles R Greathouse IV, Oct 16 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, Apr 02 2005
STATUS
approved