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A334551
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Number of fixed polyominoes with 2n-1 cells and width and height both equal to n.
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2
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1, 4, 25, 120, 497, 1924, 7265, 27288, 102745, 388692, 1477721, 5643064, 21632785, 83204260, 320932177, 1240939448, 4808642313, 18668848852, 72601081385, 282762109272, 1102772229313, 4306062994148, 16832791708257, 65867445819160, 257980829463017
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OFFSET
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1,2
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COMMENTS
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A polyomino with width and height equal to n must have at least 2n-1 cells.
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..500
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FORMULA
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a(n) = 2*binomial(2*(n-1), n-1) + 4*(n-2) + (n-2)^2*(2*n-5) + 2*Sum_{i=1..n-2} Sum_{j=1..n-2} ((n-2-i)*(n-2-j)+2)*binomial(i+j, i) for n > 1.
a(n) = 8*binomial(2*(n-1), n-1) - 3*n^2 + 4*n - 8. - Peter J. Taylor, Dec 15 2020
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EXAMPLE
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a(3) = 25. Up to rotation and reflection there are 6 possibilities:
X X X X X X
X X X X X X X X X X X X X X X
X X X X X X X X X
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PROG
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(PARI) a(n) = 8*binomial(2*(n-1), n-1) - 3*n^2 + 4*n - 8; \\ Peter J. Taylor, Dec 15 2020
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CROSSREFS
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Main diagonal of A334552.
Cf. A268404.
Sequence in context: A327646 A244746 A110051 * A273023 A013187 A069639
Adjacent sequences: A334548 A334549 A334550 * A334552 A334553 A334554
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KEYWORD
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nonn
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AUTHOR
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Andrew Howroyd, Jun 06 2020
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STATUS
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approved
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