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A178208 Number of ways to choose three points in an (n X n)-grid (or geoplane). 5
0, 4, 84, 560, 2300, 7140, 18424, 41664, 85320, 161700, 287980, 487344, 790244, 1235780, 1873200, 2763520, 3981264, 5616324, 7775940, 10586800, 14197260, 18779684, 24532904, 31684800, 40495000, 51257700 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..26.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1)

FORMULA

a(n) = A000938(n) + A045996(n).

a(n) = binomial(n^2,3) = 1/6*n^2*(n^2-1)*(n^2-2). - Martin Renner, May 23 2010

G.f.: 4*x^2*(1+x)*(1+13*x+x^2)/(1-x)^7. [Colin Barker, Jan 19 2012]

a(1)=0, a(2)=4, a(3)=84, a(4)=560, a(5)=2300, a(6)=7140, a(7)=18424, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Harvey P. Dale, Nov 09 2012

MATHEMATICA

Binomial[Range[30]^2, 3] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 4, 84, 560, 2300, 7140, 18424}, 30] (* Harvey P. Dale, Nov 09 2012 *)

PROG

(PARI) a(n)=binomial(n^2, 3) \\ Charles R Greathouse IV, Feb 19 2017

CROSSREFS

Cf. A045996, A000938.

Sequence in context: A231741 A172138 A282588 * A069441 A203095 A006344

Adjacent sequences:  A178205 A178206 A178207 * A178209 A178210 A178211

KEYWORD

easy,nice,nonn

AUTHOR

Martin Renner, May 22 2010

EXTENSIONS

Extended by Ray Chandler, May 03 2011

Corrected by Harvey P. Dale, Nov 09 2012

STATUS

approved

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Last modified December 10 23:33 EST 2018. Contains 318049 sequences. (Running on oeis4.)