OFFSET
1,3
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).
FORMULA
a(n) = (n^4 + 2*n^3 + 8*n^2 - 8*n )/48; if n even.
a(n) = (n^4 + 2*n^3 + 8*n^2 - 2*n - 9)/48; if n odd.
G.f.: -x^2*(x^3-x^2+x+1) / ((x-1)^5*(x+1)^2). - Colin Barker, Jul 12 2013
EXAMPLE
for n = 3 there are the following 4 choices of 2 points (X) (rotations and reflections being ignored):
X X X .
X . . . . . X X
. . . X . . . X . . . .
MATHEMATICA
Table[b = n^4 + 2*n^3 + 8*n^2; If[EvenQ[n], c = b - 8*n, c = b - 2*n - 9]; c/48, {n, 43}] (* T. D. Noe, Jul 09 2013 *)
CoefficientList[Series[-x (x^3 - x^2 + x + 1) / ((x - 1)^5 (x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 02 2013 *)
LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 1, 4, 10, 22, 41, 72}, 50] (* Harvey P. Dale, May 11 2019 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Heinrich Ludwig, Jul 07 2013
STATUS
approved