\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-2.8) node[]{$j$};

				}
				\foreach \t in {-20,-16,-12, -8, -4, 0, 4, 8,12,16}
				{
					\fill (\t,\y-2.8) 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) node[above]{$\cdots$};
				\fill (+9,\y+8) node[above]{$Reg_{-k+2m-1}$};
				\fill (+1,\y+8) node[above]{$\cdots$};
				\fill (-7,\y+8) node[above]{$Reg_{1}$};
				\fill (-11,\y+8) node[above]{$Reg_{0}$};
				\fill (-15,\y+8) node[above]{$Reg_{-1}$};
				\fill (-19,\y+8) node[above]{$Reg_{-2}$};
			


				\draw[very thick]  plot[rounded corners] coordinates {(-12,\y-2) (-12,\y+6)(-20,\y+8)(-20,\y+6)(10,\y-2)};
				\draw plot[rounded corners] coordinates {(-8,\y-2) (-8,\y+6)(-16,\y+8)(-16,\y+6)(14,\y-2)};
				\draw plot[rounded corners] coordinates {(-4,\y-2) (-4,\y+6)(-12,\y+8)(-12,\y+6)(18,\y-2)};
				\draw plot[rounded corners] coordinates {(0,\y-2) (0,\y+6)(-8,\y+8)(-8,\y+6)(19,\y-1.2)};
				\draw plot[rounded corners] coordinates {(4,\y-2) (4,\y+6)(-4,\y+8)(-4,\y+6)(19,\y-.13)};
				\draw plot[rounded corners] coordinates {(8,\y-2) (8,\y+6)(-0,\y+8)(-0,\y+6)(19,\y+.94)};
				\draw plot[rounded corners] coordinates {(12,\y-2) (12,\y+6)(4,\y+8)(4,\y+6)(19,\y+2.01)};
				\draw plot[rounded corners] coordinates {(16,\y-2) (16,\y+6)(8,\y+8)(8,\y+6)(19,\y+3.08)};
				
				\draw plot[rounded corners] coordinates {(19,\y+6.29)(12,\y+8)(12,\y+6)(19,\y+4.15)};
				\draw plot[rounded corners] coordinates {(19,\y+7.36)(16,\y+8)(16,\y+6)(19,\y+5.22)};
				
				\draw plot[rounded corners] coordinates {(-16,\y-2)(-16,\y+6)(-21,\y+7.36)};
				\draw plot[rounded corners] coordinates {(-20,\y-2)(-20,\y+6)(-21,\y+6.29)};
				\draw plot[rounded corners] coordinates {(-21,\y+5.22)(6,\y-2)};
				\draw plot[rounded corners] coordinates {(-21,\y+4.15)(2,\y-2)};
				\draw plot[rounded corners] coordinates {(-21,\y+3.08)(-2,\y-2)};
				\draw plot[rounded corners] coordinates {(-21,\y+2.01)(-6,\y-2)};
				\draw plot[rounded corners] coordinates {(-21,\y+.94)(-10,\y-2)};
				\draw plot[rounded corners] coordinates {(-21,\y-.13)(-14,\y-2)};
				\draw plot[rounded corners] coordinates {(-21,\y-1.2)(-18,\y-2)};
				
				
				
				
\draw[red] (-12,\y+6) circle (.3);
\draw[red] (-11.9,\y+6.15) node[right] {$c_0$};
}
}
\end{tikzpicture}

