Covid-19 spread

A Street has 13 houses in a row. Some resident sin the first house tested positive for Covid-19. The virus spreads in 2 ways: It can spread to the next house or jump directly to the third house. Residents of house 2 can get infected in only one way, house 3 in two ways, house four in 3 ways, house 5 in five ways and so on. If the virus progresses from left to right direction, in how many ways can house 13 be infected?

Correct answer:

n13 =  233

Step-by-step explanation:

n1=1 n2=n1=1 n3=n1+n2=1+1=2 n4=n3+n2=2+1=3 n5=n4+n3=3+2=5 n6=n5+n4=5+3=8 n7=n6+n5=8+5=13 n8=n7+n6=13+8=21 n9=n8+n7=21+13=34 n10=n9+n8=34+21=55 n11=n10+n9=55+34=89 n12=n11+n10=89+55=144 n13=n12+n11=144+89=233

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