A393596 - OEIS

A393596

Number of alternating sign matrices of size n which are sparse and full.

1, 1, 2, 7, 38, 302, 3410, 53191, 1113852, 30483102, 1066119338

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OFFSET

0,3

COMMENTS

An alternating sign matrix (ASM) is sparse if it cannot be turned into another ASM by replacing nonzero entries by zeros (cf. A392029).

An ASM is full if it cannot be turned into another ASM by replacing zero entries by nonzero entries (cf. A392410).

LINKS

EXAMPLE

The first ASM is neither sparse or full, because it can be turned into the last two by adding or removing nonzero entries:

[0 0 + 0 0 0] [0 0 + 0 0 0] [0 0 + 0 0 0]

[0 + 0 0 0 0] [0 + - + 0 0] [0 + 0 0 0 0]

[+ - 0 0 + 0] [+ - + - + 0] [+ 0 0 0 0 0]

[0 + 0 0 - +] [0 + 0 0 - +] [0 0 0 0 0 +]

[0 0 0 + 0 0] [0 0 0 + 0 0] [0 0 0 + 0 0]

[0 0 0 0 + 0] [0 0 0 0 + 0] [0 0 0 0 + 0]

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

a(8)-a(10) from Christian Sievers, Mar 06 2026

STATUS

approved