Search: id:A008867
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%I A008867
%S A008867 1,3,3,6,7,6,10,12,12,10,15,18,19,18,15,21,25,27,27,25,21,28,33,36,37,
               36,
%T A008867 33,28,36,42,46,48,48,46,42,36,45,52,57,60,61,60,57,52,45,55,63,69,73,
               75,
%U A008867 75,73,69,63,55,66,75,82,87,90,91,90,87,82,75,66,78,88,96,102,106,108
%N A008867 Triangle of truncated triangular numbers: k-th term in n-th row is number 
               of dots in hexagon of sides k, n-k, k, n-k, k, n-k.
%C A008867 Closely related to A109439. The current sequence is made of truncated 
               triangular numbers, the latter gives the full description. Both can 
               help to build a cube with layers perpendicular to the great diagonal. 
               E.g.: 15,18,19,18,15 in A008867 is a truncation of the lesser triangular 
               numbers of 1,3,6,10,15,18,19,18,15,10,6,3,1 in A109439. - M. Dauchez 
               (mdzzdm(AT)yahoo.fr), Sep 02 2005
%H A008867 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination 
               Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http:/
               /www.research.att.com/~njas/doc/ldl7.txt">Abstract</a>, <a href="http:/
               /www.research.att.com/~njas/doc/ldl7.pdf">pdf</a>, <a href="http:/
               /www.research.att.com/~njas/doc/ldl7.ps">ps</a>).
%p A008867 n*(n-3)/2 - k^2+k*n+1;
%Y A008867 Row sums are in A005900.
%Y A008867 Cf. A109439.
%Y A008867 Sequence in context: A117775 A021301 A016652 this_sequence A003879 A078565 
               A026926
%Y A008867 Adjacent sequences: A008864 A008865 A008866 this_sequence A008868 A008869 
               A008870
%K A008867 nonn,tabl,easy
%O A008867 2,2
%A A008867 N. J. A. Sloane (njas(AT)research.att.com), J. H. Conway and R. K. Guy

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