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A002625
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Expansion of 1/((1-x)^3*(1-x^2)^2*(1-x^3)).
(Formerly M2726 N1093)
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5
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1, 3, 8, 17, 33, 58, 97, 153, 233, 342, 489, 681, 930, 1245, 1641, 2130, 2730, 3456, 4330, 5370, 6602, 8048, 9738, 11698, 13963, 16563, 19538, 22923, 26763, 31098, 35979, 41451, 47571, 54390, 61971, 70371, 79660, 89901, 101171, 113540, 127092, 141904, 158068, 175668, 194804, 215568
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OFFSET
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0,2
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COMMENTS
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Number of (integer) partitions of n into 3 sorts of 1's, 2 sorts of 2's, and 1 sort of 3's. - Joerg Arndt, May 17 2013
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (3,-1,-4,2,2,2,-4,-1,3,-1).
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FORMULA
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a(n) = floor((n+1)*(135*(-1)^n + 6*n^4 + 144*n^3 + 1256*n^2 + 4744*n + 6785)/8640+1/2). - Tani Akinari, Oct 07 2012
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MAPLE
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MATHEMATICA
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CoefficientList[Series[1/((1-x)^3*(1-x^2)^2*(1-x^3)), {x, 0, 50}], x] (* Vincenzo Librandi, Feb 25 2012 *)
LinearRecurrence[{3, -1, -4, 2, 2, 2, -4, -1, 3, -1}, {1, 3, 8, 17, 33, 58, 97, 153, 233, 342}, 50] (* Harvey P. Dale, Sep 24 2022 *)
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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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STATUS
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approved
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