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

0,2

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).

Links

Table of n, a(n) for n=0..64.

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

Cf. A035513, A022344.

Sequence in context: A181184 A078383 A232644 * A272908 A191432 A135587

Adjacent sequences: A125509 A125510 A125511 * A125513 A125514 A125515

Keyword

nonn,tabl

Author

Kenneth J Ramsey, Dec 28 2006

Extensions

Edited by Dean Hickerson, Jan 14 2007

Status

approved