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A239568
Number of ways to place 2 points on a triangular grid of side n so that they are not adjacent.
8
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
M. J. Hay, J. Schiff, N. J. Fisch, Maximal energy extraction under discrete diffusive exchange, arXiv preprint arXiv:1508.03499, 2015
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
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, Mar 22 2014
STATUS
approved