Search: a059476 -id:a059476
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A005160
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Number of alternating sign n X n matrices invariant under a quarter turn.
(Formerly M0396)
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+10
4
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1, 0, 1, 2, 3, 0, 12, 40, 100, 0, 1225, 6860, 28812, 0, 1037232, 9779616
(list;
graph;
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listen;
history;
text;
internal format)
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OFFSET
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1,4
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COMMENTS
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Robbins incorrectly gives a(12) = 6460.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, A baker's dozen of conjectures concerning plane partitions, pp. 285-293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986.
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LINKS
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FORMULA
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Robbins gives a simple (conjectured) formula.
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CROSSREFS
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KEYWORD
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nonn,nice,more
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AUTHOR
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STATUS
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approved
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A005161
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Number of alternating sign 2n+1 X 2n+1 matrices symmetric with respect to both horizontal and vertical axes (VHSASM's).
(Formerly M1700)
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+10
3
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1, 1, 1, 2, 6, 33, 286, 4420, 109820, 4799134, 340879665, 42235307100, 8564558139000, 3012862604463000, 1742901718473961200, 1742218029490675762080, 2873822682985675809192288, 8167157387273280570395662320, 38402596062535617548517706584760, 310388509293255836481583597538626504
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, A baker's dozen of conjectures concerning plane partitions, pp. 285-293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986.
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LINKS
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FORMULA
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Robbins gives a simple (conjectured) formula, which was proven by Okada.
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PROG
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b(n) = prod(k=0, n-1, (3*k+2)*(6*k+3)!*(2*k+1)!/((4*k+2)!*(4*k+3)!));
c(n) = prod(k=0, n-1, (3*k+1)*(6*k)!*(2*k)!/((4*k)!*(4*k+1)!));
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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