A240445 Numbers of ways to place five indistinguishable points on an n X n square grid so that no four of them are vertices of a square of any orientation.

96, 4128, 52080, 373632, 1898064, 7604352, 25580016, 75208320, 198651024, 480768288, 1081848768, 2289041664, 4594218720, 8808178176, 16223664672, 28842649344, 49686723072, 83213333280, 135864971088, 216783321216, 338725852080, 519228378240, 782063802000

Offset: 3

Author

Heinrich Ludwig, May 09 2014

Keywords

• nonn
• easy

Comments

All elements of the sequence are multiples of 48.

Links

• Heinrich Ludwig, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Cf. A240444, A240446.

Programs

Magma

[(n^10 - 10*n^8 + 25*n^6 - 16*n^2)/120: n in [3..30]]; // Wesley Ivan Hurt, May 09 2014

Maple

A240445:=n->(n^10 - 10*n^8 + 25*n^6 - 16*n^2)/120; seq(A240445(n), n=3..30); # Wesley Ivan Hurt, May 09 2014

Mathematica

Table[(n^10 - 10*n^8 + 25*n^6 - 16*n^2)/120, {n, 3, 30}] (* Wesley Ivan Hurt, May 09 2014 *)

Formula

a(n) = (n^10 - 10*n^8 + 25*n^6 - 16*n^2)/120.

G.f.: -48*x^3*(x+1)*(2*x^4+62*x^3+187*x^2+62*x+2) / (x-1)^11. - Colin Barker, May 09 2014