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URL: https://oeis.org/A263135

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A263135
The maximum number of penny-to-penny connections when n pennies are placed on the vertices of a hexagonal tiling.
1
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
0,4
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.
EXAMPLE
. | | 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 .
CROSSREFS
Cf. A047932 (triangular tiling), A123663 (square tiling).
Sequence in context: A267306 A376665 A001959 * A119930 A173552 A188010
KEYWORD
nonn
AUTHOR
Peter Kagey, Oct 10 2015
STATUS
approved