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A193053
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a(n) = (14*n*(n+3) + (2*n-5)*(-1)^n + 21)/16.
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14
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1, 5, 10, 17, 26, 36, 49, 62, 79, 95, 116, 135, 160, 182, 211, 236, 269, 297, 334, 365, 406, 440, 485, 522, 571, 611, 664, 707, 764, 810, 871, 920, 985, 1037, 1106, 1161, 1234, 1292, 1369, 1430, 1511, 1575, 1660, 1727, 1816, 1886, 1979, 2052, 2149, 2225, 2326
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OFFSET
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0,2
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COMMENTS
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For an origin of this sequence, see the numerical spiral illustrated in the Links section.
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LINKS
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FORMULA
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O.g.f.: (1 + 4*x + 3*x^2 - x^3)/((1 + x)^2*(1 - x)^3).
E.g.f.: (1/16)*((21 + 56*x + 14*x^2)*exp(x) - (5 + 2*x)*exp(-x)). - G. C. Greubel, Aug 19 2017
a(n+2) + 2*a(n+1) + a(n) = A024966(n+2).
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MATHEMATICA
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Table[(14*n*(n + 3) + (2*n - 5)*(-1)^n + 21)/16, {n, 0, 50}] (* Vincenzo Librandi, Mar 26 2013 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 5, 10, 17, 26}, 60] (* Harvey P. Dale, Jun 19 2020 *)
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PROG
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(PARI) for(n=0, 50, print1((14*n*(n+3)+(2*n-5)*(-1)^n+21)/16", "));
(Magma) [(14*n*(n+3)+(2*n-5)*(-1)^n+21)/16: n in [0..50]];
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CROSSREFS
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Cf. A195020 (vertices of the numerical spiral in link).
Cf. A001106, A022264, A033572, A144555, A152760, A158482, A158485, A185019, A195021, A195023-A195030, A195320, A198017 [incomplete list].
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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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