We provide a combinatorial proof of a formula for the sum of evenly spaced binomial coefficients. This identity, along with a generalization, are proved by counting weighted walks on a graph.
© 2010 Mathematical Association of America
Benjamin, Arthur T., Bob Chen and Kimberly Kindred. "Sums of Evenly Spaced Binomial Coefficients." Mathematics Magazine , Vol. 83, No. 5, pp. 370-373, December 2010.