A189894 - OEIS

%I #13 Sep 22 2025 20:15:22

%S 4,50,208,582,1308,2556,4528,7460,11620,17310,24864,34650,47068,62552,

%T 81568,104616,132228,164970,203440,248270,300124,359700,427728,504972,

%U 592228,690326,800128,922530,1058460,1208880,1374784,1557200,1757188

%N Number of isosceles right triangles on a 2n X (n+1) grid.

%C (2n-1,n) diagonal through A189895.

%H R. H. Hardin, <a href="/A189894/b189894.txt">Table of n, a(n) for n = 1..71</a>

%F Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6).

%F Empirical: a(n) = -1/16 +11*n^4/8 +7*n^3/2  +3*n^2/4 -3*n/2 +(-1)^n/16 with g.f. -2*x*(2+17*x+14*x^2)/ ((1+x)*(x-1)^5). - _R. J. Mathar_, May 18 2011

%e Some solutions for n=2

%e ..0..0....2..2....2..1....1..1....0..2....3..2....3..0....2..0....0..1....1..0

%e ..0..1....2..1....2..2....0..0....0..0....2..2....2..0....1..1....1..0....0..2

%e ..1..0....3..2....3..1....0..2....2..2....3..1....3..1....3..1....1..2....3..1

%Y Cf. A189895.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 30 2011