OFFSET
0,2
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).
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).
EXAMPLE
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.
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]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Kenneth J Ramsey, Dec 28 2006
EXTENSIONS
Edited by Dean Hickerson, Jan 14 2007
STATUS
approved