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

3,1

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).

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

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 *)

Prog

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

Crossrefs

Cf. A240444, A240446.

Sequence in context: A008660 A164751 A272765 * A229458 A285171 A239182

Adjacent sequences: A240442 A240443 A240444 * A240446 A240447 A240448

Keyword

nonn,easy

Author

Heinrich Ludwig, May 09 2014

Status

approved