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A190576
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a(n) = n^2 + 5*n - 5.
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3
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1, 9, 19, 31, 45, 61, 79, 99, 121, 145, 171, 199, 229, 261, 295, 331, 369, 409, 451, 495, 541, 589, 639, 691, 745, 801, 859, 919, 981, 1045, 1111, 1179, 1249, 1321, 1395, 1471, 1549, 1629, 1711, 1795, 1881, 1969, 2059, 2151, 2245, 2341
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OFFSET
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1,2
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COMMENTS
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Also a(n) = n^2 + 9*n + 9 if the offset is changed to -1. - R. J. Mathar, May 18 2011
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LINKS
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FORMULA
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G.f.: x*(-1 - 6*x + 5*x^2) / (x-1)^3. - R. J. Mathar, May 18 2011
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=1, a(2)=9, a(3)=19. - Harvey P. Dale, May 28 2015
Sum_{n>=1} 1/a(n) = 199/495 + Pi*tan(3*sqrt(5)*Pi/2)/(3*sqrt(5)). - Amiram Eldar, Jan 18 2021
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MATHEMATICA
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k = 5; Table[n^2 + k*n - k, {n, 100}]
LinearRecurrence[{3, -3, 1}, {1, 9, 19}, 50] (* Harvey P. Dale, May 28 2015 *)
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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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