OFFSET
2,1
COMMENTS
Rotations or reflections of a placement are considered as the same. If they are distinguished, numbers are A172132.
LINKS
Heinrich Ludwig, Table of n, a(n) for n = 2..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).
FORMULA
a(n) = (n^4 - 2*n^2 + 20*n - 16 + IF(MOD(n, 2) = 1)*(2*n^2 - 4*n - 1))/16.
a(n) = (-33+(-1)^n+4*(9+(-1)^n)*n-2*(1+(-1)^n)*n^2+2*n^4)/32. - Colin Barker, Jun 10 2014
G.f.: x^2*(x^6-3*x^4-5*x^3-3*x-2) / ((x-1)^5*(x+1)^3). - Colin Barker, Jun 10 2014
MAPLE
A243717:=n->(-33+(-1)^n+4*(9+(-1)^n)*n-2*(1+(-1)^n)*n^2+2*n^4)/32; seq(A243717(n), n=2..50); # Wesley Ivan Hurt, Jun 11 2014
MATHEMATICA
Table[(-33 + (-1)^n + 4*(9 + (-1)^n)*n - 2*(1 + (-1)^n)*n^2 + 2*n^4)/
32, {n, 2, 50}] (* Wesley Ivan Hurt, Jun 11 2014 *)
PROG
(PARI) Vec(x^2*(x^6-3*x^4-5*x^3-3*x-2)/((x-1)^5*(x+1)^3) + O(x^100)) \\ Colin Barker, Jun 10 2014
(Magma) [ (-33+(-1)^n+4*(9+(-1)^n)*n-2*(1+(-1)^n)*n^2+2*n^4)/32: n in [2..50]]; // Wesley Ivan Hurt, Jun 11 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Jun 10 2014
STATUS
approved