A239568 Number of ways to place 2 points on a triangular grid of side n so that they are not adjacent.

0, 6, 27, 75, 165, 315, 546, 882, 1350, 1980, 2805, 3861, 5187, 6825, 8820, 11220, 14076, 17442, 21375, 25935, 31185, 37191, 44022, 51750, 60450, 70200, 81081, 93177, 106575, 121365, 137640, 155496, 175032, 196350, 219555, 244755, 272061, 301587, 333450, 367770

Offset

2,2

Links

Heinrich Ludwig, Table of n, a(n) for n = 2..1000

M. J. Hay, J. Schiff, N. J. Fisch, Maximal energy extraction under discrete diffusive exchange, arXiv preprint arXiv:1508.03499, 2015

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1)

Formula

a(n) = n*(n-1)*(n-2)*(n+5)/8.

G.f.: 3*x^3*(x-2) / (x-1)^5. - Colin Barker, Mar 22 2014

a(n) = Sum_{i=0..n} (i+5)*A000217(i). - Bruno Berselli, Apr 29 2014

a(n) = t(t(n,k),n) + n, where t(n,k) = n*(n+1)/2 + k*n and t(n,1) = A000096(n). - Bruno Berselli, Feb 28 2017

Prog

(PARI) concat(0, Vec(3*x^3*(x-2)/(x-1)^5 + O(x^100))) \\ Colin Barker, Mar 22 2014

Crossrefs

Cf. A239567, A032091, A239569 (3 points), A239570 (4 points), A239571 (5 points), A282998 (6 points).

Regarding the third formula, see similar sequences listed in A241765.

Sequence in context: A027276 A101970 A136105 * A198958 A027313 A217365

Adjacent sequences: A239565 A239566 A239567 * A239569 A239570 A239571

Keyword

nonn,easy

Author

Heinrich Ludwig, Mar 22 2014

Status

approved