Flatten@NestList[#+1&,{1,0},8]
{1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8}
Original Post
NestList[#+{1,1}&, {1,0},8]//Flatten
user1066
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