%\begin{center}
\begin{tikzpicture}[scale = 0.72*\ScaleForProgressionFormulaFigs]
\tikzstyle{every node} = [font = \small]
	\foreach \x in {0}
	{
	\foreach \y in {-8}
		{
	
		\draw[black,thick,->] (\x-22,\y-2) -- (\x+20,\y-2);
		
			\foreach \t in {-20,-18,-16,-14,-12,-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10,12,14,16,18}
				{
					\fill (\t,\y-2) circle (.1);

				}
				\foreach \t in {-18,-14,-10, -6, -2, 2, 6,10,14,18}
				{
					\fill (\t,\y-2.6) node[]{$j$};

				}
				\foreach \t in {-20,-16,-12, -8, -4, 0, 4, 8,12,16}
				{
					\fill (\t,\y-2.6) node[]{$i$};

				}	
				\foreach \t in {-21,-17,-13,-9, -5, -1, 3, 7, 11,15,19}
				{
					\draw[dashed] (\t,\y-2)--(\t, \y+8);

				}
			
				\fill (+17,\y+8.99) node[]{$Reg_{k-1}$};
				\fill (+1,\y+8.99) node[]{$\cdots$};
				\fill (-11,\y+8.99) node[]{$Reg_{2}$};
				\fill (-15,\y+8.99) node[]{$Reg_{1}$};
				\fill (-19,\y+8.99) node[]{$Reg_{0}$};
			
          %working on marked point $s$, going from left to right
				
				\draw[]  plot[rounded corners] coordinates {(-22,\y+7.5) (14,\y-2) };
				\draw[]  plot[rounded corners] coordinates {(-22,\y+6.5) (10,\y-2) };
				\draw[]  plot[rounded corners] coordinates {(-22,\y+5.5) (6,\y-2) };
				\draw[]  plot[rounded corners] coordinates {(-22,\y+4.5) (2,\y-2) };
				\draw[]  plot[rounded corners] coordinates {(-22,\y+3.5) (-2,\y-2) };
				\draw[]  plot[rounded corners] coordinates {(-22,\y+2.5) (-6,\y-2) };
				\draw[]  plot[rounded corners] coordinates {(-22,\y+1.5) (-10,\y-2) };
				\draw[]  plot[rounded corners] coordinates {(-22,\y+0.5) (-14,\y-2) };
				\draw[]  plot[rounded corners] coordinates {(-22,\y-0.5) (-18,\y-2) };
				
				 \draw[very thick]  plot[rounded corners] coordinates {(-20,\y-2) (-20,\y+8) (18,\y-2)};
				 \draw[]  plot[rounded corners] coordinates {(-16,\y-2) (-16,\y+8) (19,\y-1)};
				 \draw[]  plot[rounded corners] coordinates {(-12,\y-2) (-12,\y+8)(19,\y+0) };
				\draw[]  plot[rounded corners] coordinates {(-8,\y-2) (-8,\y+8)(19,\y+1) };
				\draw[]  plot[rounded corners] coordinates {(-4,\y-2) (-4,\y+8)(19,\y+2) };
				\draw[]  plot[rounded corners] coordinates {(0,\y-2) (0,\y+8)(19,\y+3) };
				\draw[]  plot[rounded corners] coordinates {(4,\y-2) (4,\y+8)(19,\y+4) };
				\draw[]  plot[rounded corners] coordinates {(8,\y-2) (8,\y+8)(19,\y+5) };
				\draw[]  plot[rounded corners] coordinates {(12,\y-2) (12,\y+8)(19,\y+6) };
				\draw[]  plot[rounded corners] coordinates {(16,\y-2) (16,\y+8)(19,\y+7) };
				
				
				
\draw[red] (-20,\y+2) circle (.3);
\draw[red] (-19.9,\y+2.15) node[right] {$c_0$};
}
}
\end{tikzpicture}
%\end{center}