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A080861
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15*n^2 + 6*n + 1.
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2
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1, 22, 73, 154, 265, 406, 577, 778, 1009, 1270, 1561, 1882, 2233, 2614, 3025, 3466, 3937, 4438, 4969, 5530, 6121, 6742, 7393, 8074, 8785, 9526, 10297, 11098, 11929, 12790, 13681, 14602, 15553, 16534, 17545, 18586, 19657, 20758, 21889, 23050
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OFFSET
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0,2
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COMMENTS
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The old definition of this sequence was "Generalized polygonal numbers".
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LINKS
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FORMULA
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a(n) = C(6,0) + C(6,1)*n + C(6,2)*n^2.
G.f.: (C(5,0)+(C(7,2)-2)*x+C(5,2)*x^2)/(1-x)^3 = (1+19*x+10*x^2)/(1-x)^3.
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MATHEMATICA
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CoefficientList[Series[(1 + 19 x + 10 x^2) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 05 2013 *)
LinearRecurrence[{3, -3, 1}, {1, 22, 73}, 40] (* Harvey P. Dale, Sep 28 2019 *)
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PROG
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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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Definition replaced with the closed form by Bruno Berselli, Jan 16 2013
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STATUS
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approved
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