A231654 Number of non-equivalent ways to choose 5 points in an equilateral triangle grid of side n.

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

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