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hi welcome to this video in todays video im going to do this problem suppose this sequence a sub 0 e sub 1 sub 2 and so on is an increasing sequence of non-negative integers such that for all integer n there is a unique triple i j k such that n is an integer equal to a sub i plus 2 times a sub j plus 4 times a sub k find a sub of 1998 this is international mathematical unemployed shortlist of 1998 okay is it written in the form of the generating sequence okay so i can think about the generating function also we can think about convolution of the product of the series okay p of the x as a as a convolution form that p x equal to the series of a to set the of the x equal to the series of the x to the a sub k as a convolution form series okay zero goes the kgo from zero the k goes from zero to infinity okay so this one i can rewrite it as a p x square equal to the sum of x x to the to the a sub k k goes from zero to plus infinity and also you can rewrite p x to the fourth equal to the s
