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

1,3

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.

Formula

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

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 *)

Crossrefs

Cf. A193416.

Sequence in context: A116650 A140205 A140206 * A158618 A000788 A053039

Adjacent sequences: A007815 A007816 A007817 * A007819 A007820 A007821

Keyword

nonn

Author

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

Status

approved