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A090288
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a(n) = 2*n^2 + 6*n + 2.
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22
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2, 10, 22, 38, 58, 82, 110, 142, 178, 218, 262, 310, 362, 418, 478, 542, 610, 682, 758, 838, 922, 1010, 1102, 1198, 1298, 1402, 1510, 1622, 1738, 1858, 1982, 2110, 2242, 2378, 2518, 2662, 2810, 2962, 3118, 3278, 3442, 3610, 3782, 3958, 4138, 4322, 4510
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OFFSET
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0,1
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COMMENTS
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Values of polynomial K_2 related to A090285: a(n) = K_2(n) = Sum_{k>=0} A090285(2,k)*2^k*binomial(n,k).
a(n) is the area of a triangle with vertices at (b(n-2),b(n-1)), (b(n),b(n+1)), and (b(n+2),B(n+3)) for b(k)=A000292(k) with n>1. - J. M. Bergot, Mar 23 2017
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LINKS
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FORMULA
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Sum_{n>=0} 1/a(n) = 1/2 + Pi*tan(sqrt(5)*Pi/2)/(2*sqrt(5)). - Amiram Eldar, Dec 23 2022
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {2, 10, 22}, 50] (* Harvey P. Dale, May 04 2017 *)
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PROG
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(Magma) [2*(1+3*n+n^2): n in [0..50]]; // G. C. Greubel, May 31 2019
(Sage) [2*(1+3*n+n^2) for n in (0..50)] # G. C. Greubel, May 31 2019
(GAP) List([0..50], n-> 2*(1+3*n+n^2)) # G. C. Greubel, May 31 2019
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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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STATUS
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approved
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