

A261212


Maximum number of 1's in an fully symmetrical n X n binary matrix with no three 1's adjacent in a line along a row, column or diagonally.


1



1, 4, 4, 8, 16, 20, 25, 36, 41, 48, 64, 72, 81, 100, 109, 120, 144, 156, 173, 196, 213, 228, 256, 272, 300, 324, 349, 368, 401, 424, 457, 484
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OFFSET

1,2


COMMENTS

Fully symmetrical refers to the four symmetry axes: horizontal, vertical and two diagonal.
Note that a(3k+2) = 4*(1+k)^2, for k=0,...,8, but a(29) = 401.


LINKS

Table of n, a(n) for n=1..32.
Giovanni Resta, Illustration of a(6)a(30)


FORMULA

a(n) <= A181018(n).
a(3k+2) >= 4*(k+1)^2.


EXAMPLE

For n=4, the matrix is
0 1 0
1 0 1
0 1 0
For n=6, the matrix is
1 1 0 0 1 1
1 0 1 1 0 1
0 1 0 0 1 0
0 1 0 0 1 0
1 0 1 1 0 1
1 1 0 0 1 1


CROSSREFS

Cf. A181018.
Sequence in context: A190100 A244421 A030168 * A112435 A232508 A028610
Adjacent sequences: A261209 A261210 A261211 * A261213 A261214 A261215


KEYWORD

nonn


AUTHOR

V.J. Pohjola and Giovanni Resta, Aug 12 2015


STATUS

approved



