cp's OEIS Frontend

A007818 Maximal number of bonds joining n nodes in simple cubic lattice.

%I A007818 #25 Aug 22 2021 19:15:10
%S A007818 0,1,2,4,5,7,9,12,13,15,17,20,21,23,25,28,30,33,34,36,38,41,43,46,48,
%T A007818 51,54,55,57,59,62,64,67,69,72,75,76,78,80,83,85,88,90,93,96,98,101,
%U A007818 104,105,107,109,112,114,117,119,122,125,127,130,133,135,138,141
%N A007818 Maximal number of bonds joining n nodes in simple cubic lattice.
%C A007818 a(n) is also the maximal number of kisses between n cubes to form a polycube. The surface area of such polycubes are A193416. - _Mohammed Yaseen_, Aug 08 2021
%H A007818 Martin Y. Veillette, <a href="/A007818/b007818.txt">Table of n, a(n) for n = 1..500</a>
%H A007818 G. Agnarsson, <a href="http://arxiv.org/abs/1106.4997">On the number of hypercubic bipartitions of an integer</a>, arXiv preprint arXiv:1106.4997 [math.CO], 2011.
%H A007818 G. Agnarsson, <a href="http://arxiv.org/abs/1112.3015">Induced subgraphs of hypercubes</a>, arXiv preprint arXiv:1112.3015 [math.CO], 2011.
%H A007818 G. Agnarsson and K. Lauria, <a href="http://arxiv.org/abs/1302.6517">Extremal subgraphs of the d-dimensional grid graph</a>, arXiv preprint arXiv:1302.6517 [math.CO], 2013.
%F A007818 a(n) = 3*n - A193416(n)/2. - _Mohammed Yaseen_, Aug 08 2021
%t A007818 qmax = 2000; sequence =
%t A007818 FoldList[Plus, 0, q = Table[3, {qmax}];
%t A007818   q[[Flatten[
%t A007818      Table[Table[{j^3 + i (i - 1), j^3 + i^2, j^2 (j + 1) + i (i + 1),
%t A007818          j^2 (j + 1) + i^2, (j + 1)^2 j + i (i + 1), (j + 1)^2 j +
%t A007818          i^2}, {i, 1, j}], {j, 0, (qmax)^(1/3) - 1}]]]]--;
%t A007818   q[[Flatten[
%t A007818      Table[{j^3, j^2 (j + 1), (j + 1)^2 j}, {j,
%t A007818        1, (qmax)^(1/3) - 1}]]]]--; q] (* _Martin Y. Veillette_, Jul 19 2011 *)
%Y A007818 Cf. A193416.
%K A007818 nonn
%O A007818 1,3
%A A007818 D. Heuer (heuer(AT)isnd23.in2p3.fr)