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A061925
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a(n) = ceiling(n^2/2) + 1.
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17
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1, 2, 3, 6, 9, 14, 19, 26, 33, 42, 51, 62, 73, 86, 99, 114, 129, 146, 163, 182, 201, 222, 243, 266, 289, 314, 339, 366, 393, 422, 451, 482, 513, 546, 579, 614, 649, 686, 723, 762, 801, 842, 883, 926, 969, 1014, 1059, 1106, 1153, 1202, 1251, 1302, 1353, 1406
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OFFSET
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0,2
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COMMENTS
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For n >= 3, a(n) is the number of square polyominoes with at least 2n - 2 cells whose bounding box has size 2 X n.
For n = 3, there are 6 square polyominoes with a bounding box of size 2 X 3:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
|_|_|_| |_|_|_| |_|_|_| |_|_|_| |_|_|_| |_|_|_
|_|_|_| |_|_| |_| |_| |_| |_| |_|_|
(End)
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LINKS
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FORMULA
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a(2*n) = a(2*n-1) + 2*n - 1 = 2*n^2 + 1 = A058331(n).
a(2*n+1) = a(2*n) + 2*n + 1 = 2*(n^2 + n + 1) = A051890(n+1).
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
G.f.: (1-x^2+2*x^3)/((1+x) * (1-x)^3). (End)
E.g.f.: ((2 + x + x^2)*cosh(x) + (3 + x + x^2)*sinh(x))/2. - Stefano Spezia, May 07 2021
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MAPLE
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MATHEMATICA
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LinearRecurrence[{2, 0, -2, 1}, {1, 2, 3, 6}, 60] (* Harvey P. Dale, Jan 03 2024 *)
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PROG
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(PARI) { for (n=0, 1000, write("b061925.txt", n, " ", ceil(n^2/2) + 1) ) } \\ Harry J. Smith, Jul 29 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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