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<TITLE>Basic questions?</TITLE>
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</SPAN><FONT COLOR="#0000EE"><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'>A108150</SPAN></FONT></FONT><SPAN STYLE='font-size:18.0px'> </SPAN><FONT COLOR="#800000"><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'>C(n+1,1)*C(n+3,1)<BR>
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</SPAN></FONT></FONT></FONT><FONT COLOR="#800000"><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'><FONT FACE="Courier, Courier New">0, 3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 195, 224, 255, 288, 323, 360, 399, 440, 483, 528, 575, 624, 675, 728, 783, 840, 899, 960, 1023, 1088, 1155, 1224, 1295, 1368, 1443, 1520, 1599, 1680, 1763, 1848, 1935, 2024, 2115, 2208, 2303, 2400, 2499, 2600</FONT><FONT FACE="Times, Times New Roman"> </FONT></SPAN></FONT><FONT FACE="Times, Times New Roman"><SPAN STYLE='font-size:18.0px'>(list)</SPAN><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'> <BR>
</SPAN></FONT><SPAN STYLE='font-size:15.0px'>OFFSET</SPAN><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'> </SPAN></FONT></FONT><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'><FONT FACE="Courier, Courier New">0,2<BR>
</FONT></SPAN></FONT><FONT FACE="Times, Times New Roman"><SPAN STYLE='font-size:15.0px'>EXAMPLE</SPAN><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'> </SPAN></FONT></FONT><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'><FONT FACE="Courier, Courier New">If n=0 then C(0+1,1)*C(0+3,1)= C(1,1)*C(3,1)=1*3=3<BR>
If n=5 then C(5+1,1)*C(5+3,1)= C(6,1)*C(8,1)=6*8=48<BR>
</FONT></SPAN></FONT><FONT FACE="Times, Times New Roman"><SPAN STYLE='font-size:15.0px'>KEYWORD</SPAN><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'> </SPAN></FONT></FONT><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'><FONT FACE="Courier, Courier New">easy,nonn<BR>
</FONT></SPAN></FONT><FONT FACE="Times, Times New Roman"><SPAN STYLE='font-size:15.0px'>AUTHOR</SPAN><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'> </SPAN></FONT></FONT><FONT SIZE="4"><SPAN STYLE='font-size:20.0px'><FONT FACE="Courier, Courier New">Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2005<BR>
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Hi,<BR>
<BR>
All terms are <a square -1> so I submitted the formula a(n-1)=(n^2)-1<BR>
verified for all terms displayed. <BR>
<BR>
But I wonder:<BR>
1) How to be shure it is verified to the infinity?<BR>
2) Should we *prove* that a formula is correct for any corresponding sequence?<BR>
<BR>
Here I would say C(i,1)= always i, so C(n+1,1)*C(n+3,1)==(n+1)(n+3)=n^2+4n+3=[(n+2)^2]-1, <BR>
which is well <a square-1>.<BR>
<BR>
[May be offset should be -1, or the first term should be removed (see exemples), and the formula would become a(n-2)=(n^2)-1]<BR>
<BR>
I ask these two questions, may be very basic ones, in this case but most of all *in general*.<BR>
<BR>
Alexandre</FONT></SPAN></FONT>
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