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%I #21 Nov 23 2015 01:44:09
%S 0,0,1,2,3,4,6,7,8,9,11,12,13,15,16,17,19,20,21,23,24,25,27,28,30,31,
%T 32,34,35,36,38,39,41,42,43,45,46,48,49,50,52,53,55,56,57,59,60,62,63,
%U 64,66,67,69,70,72,73,74,76,77,79,80,81,83,84,86,87,89,90
%N The maximum number of penny-to-penny connections when n pennies are placed on the vertices of a hexagonal tiling.
%C a(A033581(n)) = A152743(n).
%C 1 <= a(n+1) - a(n) <=2 for all n > 0.
%C Lim_{n -> infinity} a(n)/n = 3/2.
%C Conjecture: a(2*n) - A047932(n) = A216256(n) for n > 0.
%H Peter Kagey, <a href="/A263135/b263135.txt">Table of n, a(n) for n = 0..10000</a>
%e . | | o o .
%e . | o o | o o o o .
%e . o o | o o o | o o o o .
%e . o o | o o o | o o o o .
%e . o o | o o | o o o o .
%e . | | o o o o .
%e . | | o o .
%e . | | .
%e . f(6) = 6 | f(10) = 11 | f(24) = 30 .
%Y Cf. A047932 (triangular tiling), A123663 (square tiling).
%Y Cf. A033581, A152743.
%K nonn
%O 0,4
%A _Peter Kagey_, Oct 10 2015
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