Suppose that we have 4 cents stamps, 6 cents, and 10 cent stamps each in unlimit

Question

Suppose that we have 4 cents stamps, 6 cents, and 10 cent stamps each in unlimited supply. Let f(n) be the number of ways of obtaining n cents of postage if the order in which we put on stamps counts. For example f(4) = 1 f(8)=1 and f(10)=3 (one 10 cent stamp, 4 cent then 6 cent stamp, and 6 cent then 4 cent). If n>10 derive a recurrence for f(n). I got f(12) is 2 but I can figure out anything else because the next question requires me to find f(14) so I really don't know how to find f(n) from just f(4) f(8) f(10) and f(12).

Explanation / Answer

f(14)==> no of ways obtaining 14 cents f(4)=1 f(6)=1 f(10)=3 x1+x2+x3=14==> f(14)=f(10)+f(4) and f(6)+f(8) and f(8)+f(6)==> th combinations are 6+4+4 4+6+6 4+4+6 4+6+4 4+4+6 6+4+4 so the same repetitons are coming above so exactly total no of ways of collecting 4 is 4 6+4+4 4+6+6 4+4+6 4+6+4

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