A263135 The maximum number of penny-to-penny connections when n pennies are placed on the vertices of a hexagonal tiling.

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, 32, 34, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 50, 52, 53, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 69, 70, 72, 73, 74, 76, 77, 79, 80, 81, 83, 84, 86, 87, 89, 90

Offset: 0

Author

Peter Kagey, Oct 10 2015

Keywords

• nonn

Comments

a(A033581(n)) = A152743(n).

1 <= a(n+1) - a(n) <=2 for all n > 0.

Lim_{n -> infinity} a(n)/n = 3/2.

Conjecture: a(2*n) - A047932(n) = A216256(n) for n > 0.

Examples

			.           |            |     o o     .
.           |      o o   |  o o   o o  .
.    o o    |   o o   o  | o   o o   o .
.   o   o   |  o   o o   |  o o   o o  .
.    o o    |   o o      | o   o o   o .
.           |            |  o o   o o  .
.           |            |     o o     .
.           |            |             .
. f(6) = 6  | f(10) = 11 | f(24) = 30  .
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A047932 (triangular tiling), A123663 (square tiling).

Cf. A033581, A152743.