<PRE><B>Question 1147147</B>
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2: We can&#39;t make 2 cents with combinations of 4 and 6.  T(2) = 0&lt;br&gt;
4: We can make 4 cents only one way with 4 and 6 -- one 4-cent stamp.  T(4) = 1&lt;br&gt;
6: We can make 6 cents only one way with 4 and 6 -- one 6-cent stamp.  T(6) = 1&lt;br&gt;
8: We can make 8 cents only by adding a 4-cent stamp to an earlier total of 4 cents, or by adding a 6-cent stamp to an earlier total of 2 cents.  T(8) = T(4)+T(2) = 1+0 = 1.&lt;br&gt;
10: We can make 10 cents only by adding a 4-cent stamp to an earlier total of 6 cents, or by adding a 6-cent stamp to an earlier total of 4 cents.  T(10) = T(6)+T(4) = 1+1 = 2.&lt;br&gt;
12: We can make 12 cents only by adding a 4-cent stamp to an earlier total of 8 cents, or by adding a 6-cent stamp to an earlier total of 6 cents.  T(12) = T(8)+T(6) = 1+1 = 2.&lt;br&gt;
14: We can make 14 cents only by adding a 4-cent stamp to an earlier total of 10 cents, or by adding a 6-cent stamp to an earlier total of 8 cents.  T(14) = T(10)+T(8) = 2+1 = 3.&lt;br&gt;
Clearly the pattern will continue.  So a recursive formula for T(n) -- valid of course only for even values of n -- is&lt;br&gt;
T(n) = T(n-4)+T(n-6)&lt;br&gt;
Note that it might be better, since the formula is only valid for even integers, to write it as&lt;br&gt;
T(2n) = T(2n-4)+T(2n-6)&lt;br&gt;
The first several terms of the sequence, found recursively, are&lt;br&gt;
0,1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,...
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