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
Links
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1)
Programs
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Maple
a:= proc(n) binomial(n^2, 4) end: seq(a(n), n=1..35);
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Maxima
makelist(binomial(n^2, 4), n, 1, 56); /* Martin Ettl, Oct 15 2012 */
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