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A189345 Number of ways to choose four points in an n X n grid (or geoplane). 6
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 (list; graph; refs; listen; history; text; internal format)
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 A196414

Adjacent sequences:  A189342 A189343 A189344 * A189346 A189347 A189348

KEYWORD

nonn,easy

AUTHOR

Martin Renner, Apr 20 2011

STATUS

approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)