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A273366
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a(n) = 10*n^2 + 10*n + 2.
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7
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2, 22, 62, 122, 202, 302, 422, 562, 722, 902, 1102, 1322, 1562, 1822, 2102, 2402, 2722, 3062, 3422, 3802, 4202, 4622, 5062, 5522, 6002, 6502, 7022, 7562, 8122, 8702, 9302, 9922, 10562, 11222, 11902, 12602, 13322, 14062, 14822, 15602
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OFFSET
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0,1
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COMMENTS
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These are the numbers k such that 10*k+5 is a perfect square.
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LINKS
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FORMULA
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G.f.: 2*(x^2+8x+1)/(1-x)^3.
E.g.f.: 2*(1 + 10*x + 5*x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
Sum_{n>=0} 1/a(n) = Pi/(2*sqrt(5)) * tan(Pi/(2*sqrt(5))) (A350760). - Amiram Eldar, Jan 20 2022
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {2, 22, 62}, 50] (* G. C. Greubel, May 20 2016 *)
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PROG
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CROSSREFS
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Cf. A033583 (perfect squares ending in 0 in base 10 with final 0 removed).
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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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