A118040 - OEIS

%I #4 Mar 30 2012 18:36:56

%S 1,2,1,6,4,1,16,14,6,1,44,44,24,8,1,116,130,84,36,10,1,294,364,270,

%T 136,50,12,1,748,990,780,476,200,66,14,1,1794,2540,2268,1400,760,276,

%U 84,16,1,4352,6514,5832,4332,2260,1134,364,104,18,1,10072,15640,15876,11128

%N Triangle T, read by rows, equal to the matrix square of A118032 and also equal to a diagonal bisection of A118032; i.e., diagonal n of T equals diagonal 2n of A118032: T(n,k) = A118032(2n-k,k) for n>=k>=0.

%C Rows of this triangle form even-indexed antidiagonals of A118032; thus the row sums form a bisection of the antidiagonal sums of A118032.

%e Triangle T begins:

%e 1;

%e 2, 1;

%e 6, 4, 1;

%e 16, 14, 6, 1;

%e 44, 44, 24, 8, 1;

%e 116, 130, 84, 36, 10, 1;

%e 294, 364, 270, 136, 50, 12, 1;

%e 748, 990, 780, 476, 200, 66, 14, 1;

%e 1794, 2540, 2268, 1400, 760, 276, 84, 16, 1;

%e 4352, 6514, 5832, 4332, 2260, 1134, 364, 104, 18, 1;

%e 10072, 15640, 15876, 11128, 7410, 3396, 1610, 464, 126, 20, 1; ...

%e and is the matrix square of triangle A118032, which starts:

%e 1;

%e 1, 1;

%e 2, 2, 1;

%e 3, 4, 3, 1;

%e 6, 8, 6, 4, 1;

%e 9, 14, 15, 8, 5, 1;

%e 16, 28, 24, 24, 10, 6, 1;

%e 26, 44, 57, 36, 35, 12, 7, 1;

%e 44, 86, 84, 96, 50, 48, 14, 8, 1; ...

%e where even-indexed diagonals of A118032 form the diagonals of T.

%Y Columns: A118041, A118042, A118043; A118044 (row sums); related triangles: A118032, A118045.

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Apr 10 2006