Search: id:A100583
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%I A100583
%S A100583 0,8,44,124,268,492,816,1256,1832,2560,3460,4548,5844,7364,9128,11152,
%T A100583 13456,16056,18972,22220,25820,29788,34144,38904,44088,49712,55796,
%U A100583 62356,69412,76980,85080,93728,102944,112744,123148,134172,145836
%N A100583 a(n) = 3*n^3+(9/2)*n^2+n+(1/4)*(-1)^n-1/4.
%C A100583 Conjectured to be the number of triangles in an n X n grid of squares 
               with all diagonals drawn.
%C A100583 I contacted the author, Floor van Lamoen, but he is not aware of a proof 
               that this sequence actually gives the number of triangles in an n 
               X n grid of squares with diagonals. Robbert van der Kruk (robbertvdkruk(AT)live.nl), 
               Oct 28 2009
%H A100583 Author?, <a href="http://www.wisfaq.nl/showrecord3.asp?id=30042">WisFaq 
               (Dutch)</a>
%F A100583 a(n) = 4*Sum{i=1 to n}[i^2 + (n+1-i)*(n+1-round(i/2))].
%Y A100583 Sequence in context: A046329 A046377 A075816 this_sequence A036464 A000938 
               A165618
%Y A100583 Adjacent sequences: A100580 A100581 A100582 this_sequence A100584 A100585 
               A100586
%K A100583 nonn,new
%O A100583 0,2
%A A100583 Floor van Lamoen (fvlamoen(AT)hotmail.com), Nov 30 2004
%E A100583 In view of Robbert van der Kruk's comment, I have used the first formula 
               as the definition, and stated the number of triangles connection 
               as a conjecture. - njas, Nov 01 2009

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