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A100536
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a(n) = 3*n^2 - 2.
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17
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1, 10, 25, 46, 73, 106, 145, 190, 241, 298, 361, 430, 505, 586, 673, 766, 865, 970, 1081, 1198, 1321, 1450, 1585, 1726, 1873, 2026, 2185, 2350, 2521, 2698, 2881, 3070, 3265, 3466, 3673, 3886, 4105, 4330, 4561, 4798, 5041, 5290, 5545, 5806, 6073, 6346, 6625
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OFFSET
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1,2
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COMMENTS
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Integers k such that 3*k + 6 is a perfect square. - Gary Detlefs, Feb 22 2010
Binomial transform of (1, 9, 6, 0, 0, 0, 0, 0, 0, 0, ...). - Philippe Deléham, Mar 16 2014
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LINKS
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FORMULA
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G.f.: x*(1+7*x-2*x^2) / (1-x)^3. - R. J. Mathar, Oct 03 2011
-a(n) = (k-1)^2 + k^2 + (k+1)^2, where k = n*sqrt(-1). - Bruno Berselli, Jan 24 2014
a(n+1) = binomial(n,0) + 9*binomial(n,1) + 6*binomial(n,2). - Philippe Deléham, Mar 16 2014
E.g.f.: 2 - (2 - 3*x - 3*x^2)*exp(x). - G. C. Greubel, Mar 27 2023
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EXAMPLE
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a(2)=10 after the evaluation of a(2) = 3*(2^2) - 2 = 3*(4) - 2 = 12 - 2 = 10.
a(1) = 1*1 = 1;
a(2) = 1*1 + 9*1 = 10;
a(3) = 1*1 + 9*2 + 6*1 = 25;
a(4) = 1*1 + 9*3 + 6*3 = 46;
a(5) = 1*1 + 9*4 + 6*6 = 73; etc. (End)
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MATHEMATICA
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CoefficientList[Series[x (1+7x-2x^2)/(1-x)^3, {x, 0, 50}], x] (* or *) LinearRecurrence[{3, -3, 1}, {1, 10, 25}, 50] (* Harvey P. Dale, Nov 20 2023 *)
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PROG
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(SageMath) [3*n^2 -2 for n in range(1, 51)] # G. C. Greubel, Mar 27 2023
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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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Tyler J Newman (Tylerjnewman(AT)adelphia.net), Nov 27 2004
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STATUS
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approved
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