cp's OEIS Frontend

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.

%I A125512 #8 Jun 24 2014 01:08:37
%S A125512 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,
%T A125512 36,25,19,38,85,76,70,58,41,31,21,61,137,123,114,94,67,50,34,25,99,
%U A125512 222,199,184,152,108,81,56,40,28,161,360,322,298,246,175,132,90,65,45
%N 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.
%C A125512 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).
%F A125512 For j>1, x(i,j) = x(i,j-1) + x(i,j-2) + (T(i,j-1)*T(i,j-2) mod 2).
%e A125512 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.
%t A125512 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]
%Y A125512 Cf. A035513, A022344.
%K A125512 nonn,tabl
%O A125512 0,2
%A A125512 _Kenneth J Ramsey_, Dec 28 2006
%E A125512 Edited by _Dean Hickerson_, Jan 14 2007