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A290724 Triangle read by rows: T(n,k) = number of arrangements of k non-attacking rooks on an n X n right triangular board with every square controlled by at least one rook. 2
1, 1, 1, 0, 4, 1, 0, 2, 11, 1, 0, 0, 18, 26, 1, 0, 0, 6, 100, 57, 1, 0, 0, 0, 96, 444, 120, 1, 0, 0, 0, 24, 900, 1734, 247, 1, 0, 0, 0, 0, 600, 6480, 6246, 502, 1, 0, 0, 0, 0, 120, 8520, 39762, 21320, 1013, 1, 0, 0, 0, 0, 0, 4320, 90600, 219312, 70128, 2036, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

See A146304 for algorithm and PARI code to produce this sequence.

Equivalently, the number of maximal independent vertex sets in the n-triangular honeycomb bishop graph with k vertices. A bishop can move along two axis in the triangular honeycomb grid.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275

Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set

EXAMPLE

Triangle begins:

1;

1, 1;

0, 4,  1;

0, 2, 11,  1;

0, 0, 18,  26,  1;

0, 0,  6, 100,  57,    1;

0, 0,  0,  96, 444,  120,     1;

0, 0,  0,  24, 900, 1734,   247,     1;

0, 0,  0,  0,  600, 6480,  6246,   502,    1;

0, 0,  0,  0,  120, 8520, 39762, 21320, 1013, 1;

...

CROSSREFS

Row sums are A290615.

Cf. A259691, A259697.

Sequence in context: A206799 A084119 A166073 * A283879 A216178 A122899

Adjacent sequences:  A290721 A290722 A290723 * A290725 A290726 A290727

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Aug 09 2017

STATUS

approved

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Last modified November 17 05:27 EST 2019. Contains 329217 sequences. (Running on oeis4.)