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A239569 Number of ways to place 3 points on a triangular grid of side n so that no two of them are adjacent. 7
0, 1, 21, 151, 615, 1845, 4571, 9926, 19566, 35805, 61765, 101541, 160381, 244881, 363195, 525260, 743036, 1030761, 1405221, 1886035, 2495955, 3261181, 4211691, 5381586, 6809450, 8538725, 10618101, 13101921, 16050601, 19531065, 23617195, 28390296, 33939576 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

Rotations and reflections of placements are counted. If they are to be ignored, see A239573.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

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

FORMULA

a(n) = (n-1)*(n-2)*(n^4+6*n^3-23*n^2-92*n+264)/48.

G.f.: -x^3*(11*x^4-36*x^3+25*x^2+14*x+1) / (x-1)^7. - Colin Barker, Mar 22 2014

MATHEMATICA

CoefficientList[Series[- x (11 x^4 - 36 x^3 + 25 x^2 + 14 x + 1)/(x - 1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 23 2014 *)

PROG

(PARI) concat(0, Vec(-x^3*(11*x^4-36*x^3+25*x^2+14*x+1)/(x-1)^7 + O(x^100))) \\ Colin Barker, Mar 22 2014

(MAGMA) [(n^2-3*n+2)*(n^4+6*n^3-23*n^2-92*n+264)/48: n in [2..40]]; // Vincenzo Librandi, Mar 23 2014

CROSSREFS

Cf. A239567, A239573, A239568 (2 points), A239570 (4 points), A239571 (5 points), A282998 (6 points).

Sequence in context: A041850 A239123 A241697 * A219599 A221694 A229262

Adjacent sequences:  A239566 A239567 A239568 * A239570 A239571 A239572

KEYWORD

nonn,easy

AUTHOR

Heinrich Ludwig, Mar 22 2014

STATUS

approved

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Last modified April 25 00:46 EDT 2017. Contains 285346 sequences.