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A231654 Number of non-equivalent ways to choose 5 points in an equilateral triangle grid of side n. 3
0, 0, 2, 48, 526, 3450, 16536, 63104, 204202, 580669, 1491096, 3520768, 7754502, 16098425, 31770760, 59998736, 109022244, 191454654, 326158974, 540703008, 874630262, 1383621756, 2144889472, 3263884272, 4882793214, 7190910467, 10437526372, 14947411024 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Heinrich Ludwig, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-10,-10,50,-34,-66,110,0,-110,66,34,-50,10,10,-6,1).

FORMULA

a(n) = (n^10 + 5*n^9 - 10*n^8 - 70*n^7 + 25*n^6 + 584*n^5 - 420*n^4 - 480*n^3 - 1216*n^2 + 1536*n + B)/23040 where B = 375*n^4 - 1170*n^3 + 210*n^2 - 405*n + 1035 if n odd, and B = 0 if n even.

G.f.: x^3*(x^11 -4*x^10 +14*x^9 -78*x^8 -189*x^7 -902*x^6 -1316*x^5 -1476*x^4 -794*x^3 -258*x^2 -36*x -2) / ((x -1)^11*(x +1)^5). - Colin Barker, Feb 15 2014

MATHEMATICA

Table[If[EvenQ[n], b = 0, b = 375*n^4 - 1170*n^3 + 210*n^2 - 405*n + 1035]; (n^10 + 5*n^9 - 10*n^8 - 70*n^7 + 25*n^6 + 584*n^5 - 420*n^4 - 480*n^3 - 1216*n^2 + 1536*n + b)/23040, {n, 30}] (* T. D. Noe, Nov 14 2013 *)

CROSSREFS

Cf. A001399, A227327, A230723, A231653, A231655.

Sequence in context: A215186 A058090 A051252 * A005429 A035606 A157057

Adjacent sequences:  A231651 A231652 A231653 * A231655 A231656 A231657

KEYWORD

nonn,easy

AUTHOR

Heinrich Ludwig, Nov 13 2013

STATUS

approved

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Last modified August 14 10:47 EDT 2020. Contains 336480 sequences. (Running on oeis4.)