A189345 Number of ways to choose four points in an n X n grid (or geoplane).

0, 1, 126, 1820, 12650, 58905, 211876, 635376, 1663740, 3921225, 8495410, 17178876, 32795126, 59626385, 103962600, 174792640, 284660376, 450710001, 695946630, 1050739900, 1554599970, 2258257001, 3226076876, 4538847600, 6296972500, 8624108025, 11671285626

Offset

1,3

Links

Table of n, a(n) for n=1..27.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1)

Formula

a(n) = binomial(n^2,4) = (1/24)*n^2*(n^2-1)*(n^2-2)*(n^2-3).

G.f.: x^2*(1+x)*(1+116*x+606*x^2+116*x^3+x^4)/(1-x)^9. - Colin Barker, Jan 19 2012

Maple

a:= proc(n) binomial(n^2, 4) end: seq(a(n), n=1..35);

Prog

(Maxima)
makelist(binomial(n^2, 4), n, 1, 56); /* Martin Ettl, Oct 15 2012 */

Crossrefs

Cf. A175383, A189346.

Sequence in context: A249320 A267628 A304559 * A255177 A172140 A331100

Adjacent sequences: A189342 A189343 A189344 * A189346 A189347 A189348

Keyword

nonn,easy

Author

Martin Renner, Apr 20 2011

Status

approved