AMC 12 2007a Problem 25

Call a set of integers ''spacy'' if it contains no more than one out of any three consecutive integers. How many subsets of $\{1,2,3,\ldots,12\},$ including the empty set, are spacy?

$\mathrm{(A)}\ 121 \mathrm{(B)}\ 123 \mathrm{(C)}\ 125 \mathrm{(D)}\ 127 \mathrm{(E)}\ 129$