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A336288
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Numbers of squares formed by this procedure on n-th step: Step 1, draw a unit square. Step n, draw a unit square with center in every intersection of lines of the figure in step n-1.
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2
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1, 10, 43, 116, 245, 446, 735, 1128, 1641, 2290, 3091, 4060, 5213, 6566, 8135, 9936, 11985, 14298, 16891, 19780, 22981, 26510, 30383, 34616, 39225, 44226, 49635, 55468, 61741, 68470, 75671, 83360, 91553, 100266, 109515, 119316, 129685, 140638, 152191, 164360, 177161
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OFFSET
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1,2
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LINKS
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Ilario Miriello, Step 1,2,3, Youtube video, Jul 16 2020.
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FORMULA
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a(n) = (8*n^3 - 12*n^2 + 7*n)/3.
G.f.: x*(1 + 3*x)^2 / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
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MATHEMATICA
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Table[(8*n^3 - 12*n^2 + 7*n)/3, {n, 1, 50}] (* Amiram Eldar, Jul 16 2020 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 10, 43, 116}, 50] (* Harvey P. Dale, Sep 12 2021 *)
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PROG
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(Magma) [(8*n^3 - 12*n^2 + 7*n)/3 : n in [1..50]]; // Wesley Ivan Hurt, Jul 16 2020
(PARI) a(n) = (8*n^3 - 12*n^2 + 7*n)/3; \\ Michel Marcus, Jul 16 2020
(PARI) Vec(x*(1 + 3*x)^2 / (1 - x)^4 + O(x^40)) \\ Colin Barker, Jul 17 2020
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CROSSREFS
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KEYWORD
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nonn,easy,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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