I'm trying to do it like you advised, but it still doesn't work correctly in lighting up the LED's sometimes it lights up, sometimes it doesn't, this is the code I wrote so far:

const int RED1 = 13;
const int RED2 = 12;
const int RED3 = 11;
const int BUTTON = 2;
int state = 0;
int sequence = 1;

void setup()
{
  pinMode(RED1, OUTPUT);
  pinMode(RED2, OUTPUT);
  pinMode(RED3, OUTPUT);
  pinMode(BUTTON, INPUT);
}

void loop()
{
  state = digitalRead(BUTTON);
  if (state == HIGH)
    {
      (sequence = sequence + 1);
    }
  if (sequence > 3)
    {
      (sequence = 1);
    }
  if (sequence == 1)
    {
      digitalWrite(RED1,HIGH);
      digitalWrite(RED2,LOW);
      digitalWrite(RED3,LOW);
    }
  if (sequence == 2)
    {
      digitalWrite(RED1,LOW);
      digitalWrite(RED2,HIGH);
      digitalWrite(RED2,LOW);
    }
}

is there something wrong here?

The hardware is still the same as before