A125512 Array x read by diagonals, where x(i,j) = floor((T(i,j-1)+T(i,j+1))/2) for i>=0 and j>=0. Here T is Wythoff's array A035513.

1, 2, 5, 3, 7, 7, 5, 12, 11, 10, 9, 20, 18, 16, 14, 14, 32, 29, 27, 22, 16, 23, 52, 47, 43, 36, 25, 19, 38, 85, 76, 70, 58, 41, 31, 21, 61, 137, 123, 114, 94, 67, 50, 34, 25, 99, 222, 199, 184, 152, 108, 81, 56, 40, 28, 161, 360, 322, 298, 246, 175, 132, 90, 65, 45

Offset: 0

Author

Kenneth J Ramsey, Dec 28 2006

Keywords

• nonn
• tabl

Comments

x(i,j)*(x(i,j) + (T(i,j) mod 2)) = (5*T(i,j)^2 - (T(i,j) mod 2))/4 + A(i)*(-1)^j, where A(i)=A022344(i).

Examples

			x(2,4)=floor((T(2,3)+T(2,5))/2)=floor((26+68)/2)=47. Since T(2,4)=42 and A(2)=4, the equation in the first comment becomes 47*(47+0) = (5*42^2-0)/4 + 4*(-1)^4.
		

Crossrefs

Cf. A035513, A022344.

Programs

Mathematica

T[i_,j_]:=i*Fibonacci[j+1]+Fibonacci[j+2]*Floor[(i+1)(1+Sqrt[5])/2]; x[i_,j_]:=Floor[(T[i,j-1]+T[i,j+1])/2]

Formula

For j>1, x(i,j) = x(i,j-1) + x(i,j-2) + (T(i,j-1)*T(i,j-2) mod 2).

Extensions

Edited by Dean Hickerson, Jan 14 2007