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A060354
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The n-th n-gonal number: a(n) = n*(n^2 - 3*n + 4)/2.
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37
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0, 1, 2, 6, 16, 35, 66, 112, 176, 261, 370, 506, 672, 871, 1106, 1380, 1696, 2057, 2466, 2926, 3440, 4011, 4642, 5336, 6096, 6925, 7826, 8802, 9856, 10991, 12210, 13516, 14912, 16401, 17986, 19670, 21456, 23347, 25346, 27456, 29680, 32021
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OFFSET
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0,3
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COMMENTS
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Binomial transform of (0,1,0,3,0,0,0,...). - Paul Barry, Sep 14 2006
Also the number of permutations of length n which can be sorted by a single cut-and-paste move (in the sense of Cranston, Sudborough, and West). - Vincent Vatter, Aug 21 2013
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LINKS
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FORMULA
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a(n) = (n*(n-2)^2 + n^2)/2.
E.g.f.: exp(x)*x*(1+x^2/2). - Paul Barry, Sep 14 2006
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MAPLE
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(n*(n-2)^2+n^2)/2 ;
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MATHEMATICA
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Table[(n (n-2)^2+n^2)/2, {n, 0, 50}] (* Harvey P. Dale, Aug 05 2011 *)
CoefficientList[Series[x (1 - 2 x + 4 x^2) / (1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Feb 16 2015 *)
Table[PolygonalNumber[n, n], {n, 0, 50}] (* Harvey P. Dale, Mar 07 2016 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 2, 6}, 50] (* Harvey P. Dale, Mar 07 2016 *)
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PROG
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(PARI) { for (n=0, 1000, write("b060354.txt", n, " ", (n*(n - 2)^2 + n^2)/2); ) } \\ Harry J. Smith, Jul 04 2009
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Hareendra Yalamanchili (hyalaman(AT)mit.edu), Apr 01 2001
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STATUS
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approved
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