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A033816
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a(n) = 2*n^2 + 3*n + 3.
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20
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3, 8, 17, 30, 47, 68, 93, 122, 155, 192, 233, 278, 327, 380, 437, 498, 563, 632, 705, 782, 863, 948, 1037, 1130, 1227, 1328, 1433, 1542, 1655, 1772, 1893, 2018, 2147, 2280, 2417, 2558, 2703, 2852, 3005, 3162, 3323, 3488, 3657, 3830, 4007, 4188, 4373, 4562
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OFFSET
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0,1
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COMMENTS
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For n >= 1, a(n) is the (1,1)-th entry in a (2*n+1) X (2*n+1) magic square built using the "north-east" technique. [Most probably the author is referring to the "Siamese method" described in the Wikipedia article. - Petros Hadjicostas, Jul 26 2020~]
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: (3 - x + 2*x^2)/(1 - x)^3. (End)
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MATHEMATICA
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CoefficientList[Series[(3-x+2*x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 07 2012 *)
LinearRecurrence[{3, -3, 1}, {3, 8, 17}, 50] (* Harvey P. Dale, May 07 2015 *)
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PROG
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(Magma) I:=[3, 8, 17]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jul 07 2012
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Olivier Gorin (gorin(AT)roazhon.inra.fr)
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EXTENSIONS
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STATUS
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approved
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