document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1147147>Question 1147147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let T(n) denote the number of distinct ways that a postage of n<BR>\n" );
document.write( "cents, where n ≥ 4 and n is even, can be made by 4-cent and 6-cent stamps.<BR>\n" );
document.write( "For example, if n = 12, then we can use 3 4-cent stamps or 2 6-cent stamps,<BR>\n" );
document.write( "and there are no other possible ways. So T(12) = 2. Give a recursive solution to compute T(n) for n ≥ 4 and n is even.  </SPAN>\n" );
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document.write( "2: We can't make 2 cents with combinations of 4 and 6.  T(2) = 0<br><BR>\n" );
document.write( "4: We can make 4 cents only one way with 4 and 6 -- one 4-cent stamp.  T(4) = 1<br><BR>\n" );
document.write( "6: We can make 6 cents only one way with 4 and 6 -- one 6-cent stamp.  T(6) = 1<br><BR>\n" );
document.write( "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.<br><BR>\n" );
document.write( "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.<br><BR>\n" );
document.write( "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.<br><BR>\n" );
document.write( "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.<br><BR>\n" );
document.write( "Clearly the pattern will continue.  So a recursive formula for T(n) -- valid of course only for even values of n -- is<br><BR>\n" );
document.write( "T(n) = T(n-4)+T(n-6)<br><BR>\n" );
document.write( "Note that it might be better, since the formula is only valid for even integers, to write it as<br><BR>\n" );
document.write( "T(2n) = T(2n-4)+T(2n-6)<br><BR>\n" );
document.write( "The first several terms of the sequence, found recursively, are<br><BR>\n" );
document.write( "0,1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,...<BR>\n" );
document.write( " </SPAN>\n" );
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