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 A240826 Number of ways to choose three points on a centered hexagonal grid of size n. 2
 0, 35, 969, 7770, 35990, 121485, 333375, 790244, 1679580, 3280455, 5989445, 10349790, 17083794, 27128465, 41674395, 62207880, 90556280, 128936619, 180007425, 246923810, 333395790, 443749845, 582993719, 756884460, 971999700, 1235812175, 1556767485, 1944365094 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Hex Number. Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA a(n) = binomial(A003215(n-1), 3)      = binomial(3*n^2-3*n+1, 3)      = 1/2*n*(n-1)*(3*n^2-3*n+1)*(3*n^2-3*n-1)      = 9/2*n^6-27/2*n^5+27/2*n^4-9/2*n^3-1/2*n^2+1/2*n. G.f.: -x^2*(35*x^4+724*x^3+1722*x^2+724*x+35) / (x-1)^7. - Colin Barker, Apr 18 2014 MAPLE seq(binomial(3*n^2-3*n+1, 3), n=1..28); # Martin Renner, May 31 2014 op(PolynomialTools[CoefficientList](convert(series(-x^2*(35*x^4+724*x^3+1722*x^2+724*x+35)/(x-1)^7, x=0, 29), polynom), x)[2..29]); # Martin Renner, May 31 2014 MATHEMATICA CoefficientList[Series[- x(35 x^4 + 724 x^3 + 1722 x^2 + 724 x + 35)/(x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Apr 19 2014 *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 35, 969, 7770, 35990, 121485, 333375}, 40] (* Harvey P. Dale, Sep 12 2019 *) CROSSREFS Cf. A178208, A241219. Sequence in context: A014934 A115473 A002453 * A210313 A049395 A278723 Adjacent sequences:  A240823 A240824 A240825 * A240827 A240828 A240829 KEYWORD nonn,easy AUTHOR Martin Renner, Apr 17 2014 STATUS approved

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Last modified November 26 01:22 EST 2020. Contains 338631 sequences. (Running on oeis4.)