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A180223
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a(n) = (11*n^2 - 7*n)/2.
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9
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0, 2, 15, 39, 74, 120, 177, 245, 324, 414, 515, 627, 750, 884, 1029, 1185, 1352, 1530, 1719, 1919, 2130, 2352, 2585, 2829, 3084, 3350, 3627, 3915, 4214, 4524, 4845, 5177, 5520, 5874, 6239, 6615, 7002, 7400, 7809, 8229, 8660
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OFFSET
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0,2
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COMMENTS
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Create a triangle with T(r,1) = r^2 and T(r,c) = r^2 + r*c + c^2. The difference of the sum of the terms in row n and those in row n-1 is a(n). - J. M. Bergot, Jun 17 2013
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LINKS
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B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).
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FORMULA
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G.f.: x*(2+9*x)/(1-x)^3. - Bruno Berselli, Aug 19 2010 - corrected in Apr 18 2011
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with n>2. - Bruno Berselli, Aug 19 2010
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {0, 2, 15}, 50] (* Harvey P. Dale, Oct 10 2020 *)
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PROG
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(PARI) a(n)=1/2*(11*n^2 - 7*n);
(Sage) [n*(11*n-7)/2 for n in (0..30)] # G. C. Greubel, Sep 18 2019
(GAP) List([0..30], n-> n*(11*n-7)/2); # G. C. Greubel, Sep 18 2019
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CROSSREFS
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Cf. numbers of the form n*(n*k-k+4))/2 listed in A226488 (this sequence is the case k=11). - Bruno Berselli, Jun 10 2013
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KEYWORD
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nonn,easy
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AUTHOR
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Graziano Aglietti (mg5055(AT)mclink.it), Aug 16 2010
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STATUS
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approved
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