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It is a combination of two sequence of + 1 and + 2 addition

0 , 0 , 1 , 2 ,2 ,4 ,3 ,6 ,4 adding +1 ;;; 0 , 1 , 2 . 3 , 4 and adding + 2 :: 0 , 2 , 4 , 6 . , so next term is 8 ;;; all even numbered terms all odd numbered terms

This series 0,0,1,2,2,4,3,6,4,? contain two series 0,1,2,3,4...(add +1 for next term ) and 0,2,4,6,...(add +2 for next term ) so next term is 8.

b1*a1=c1; b2*a2=c2; c2-c1=e1; b3*a3=c3; c3-c2=e2; etc

0*0=0; 1*0=0; 0-0=0; 2*1=2; 2-0=2; 2*2=4; 4-2=2; 4*2=8; 8-4=4; 3*4=12; 12-8=4; 6*3=18; 18-12=6; 4*6=24; 24-18=6; 8 *4=32; 32-24=8

In this series contains two series normal numbers(like 0,1,2,3) and even numbers(like 0,2,4,6) and the next number is 8