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

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, 51, 54, 55, 57, 59, 62, 64, 67, 69, 72, 75, 76, 78, 80, 83, 85, 88, 90, 93, 96, 98, 101, 104, 105, 107, 109, 112, 114, 117, 119, 122, 125, 127, 130, 133, 135, 138, 141

Offset: 1

Author

D. Heuer (heuer(AT)isnd23.in2p3.fr)

Keywords

• nonn

Comments

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

Links

• Martin Y. Veillette, Table of n, a(n) for n = 1..500
• G. Agnarsson, On the number of hypercubic bipartitions of an integer, arXiv preprint arXiv:1106.4997 [math.CO], 2011.
• G. Agnarsson, Induced subgraphs of hypercubes, arXiv preprint arXiv:1112.3015 [math.CO], 2011.
• G. Agnarsson and K. Lauria, Extremal subgraphs of the d-dimensional grid graph, arXiv preprint arXiv:1302.6517 [math.CO], 2013.

Crossrefs

Cf. A193416.

Programs

Mathematica

qmax = 2000; sequence =
FoldList[Plus, 0, q = Table[3, {qmax}];
  q[[Flatten[
     Table[Table[{j^3 + i (i - 1), j^3 + i^2, j^2 (j + 1) + i (i + 1),
         j^2 (j + 1) + i^2, (j + 1)^2 j + i (i + 1), (j + 1)^2 j +
         i^2}, {i, 1, j}], {j, 0, (qmax)^(1/3) - 1}]]]]--;
  q[[Flatten[
     Table[{j^3, j^2 (j + 1), (j + 1)^2 j}, {j,
       1, (qmax)^(1/3) - 1}]]]]--; q] (* Martin Y. Veillette, Jul 19 2011 *)

Formula

a(n) = 3*n - A193416(n)/2. - Mohammed Yaseen, Aug 08 2021