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A063495
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a(n) = (2*n-1)*(5*n^2-5*n+2)/2.
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18
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1, 18, 80, 217, 459, 836, 1378, 2115, 3077, 4294, 5796, 7613, 9775, 12312, 15254, 18631, 22473, 26810, 31672, 37089, 43091, 49708, 56970, 64907, 73549, 82926, 93068, 104005, 115767, 128384, 141886, 156303, 171665, 188002, 205344
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OFFSET
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1,2
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..1000
T. P. Martin, Shells of atoms, Phys. Rep., 273 (1996), 199-241, eq. (10).
Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).
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FORMULA
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From Harvey P. Dale, Dec 18 2011: (Start)
a(1)=1, a(2)=18, a(3)=80, a(4)=217, a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) - a(n-4).
G.f.: (x^3+14*x^2+14*x+1)/(1-x)^4. (End)
E.g.f.: (-2 + 4*x + 15*x^2 + 10*x^3)*exp(x)/2 + 1. - G. C. Greubel, Dec 01 2017
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MATHEMATICA
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Table[(2n-1)(5n^2-5n+2)/2, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 18, 80, 217}, 40] (* Harvey P. Dale, Dec 18 2011 *)
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PROG
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(PARI) for (n=1, 1000, write("b063495.txt", n, " ", (2*n - 1)*(5*n^2 - 5*n + 2)/2) ) \\ Harry J. Smith, Aug 23 2009
(PARI) x='x+O('x^30); Vec(serlaplace((-2+4*x+15*x^2+10*x^3)*exp(x)/2 + 1)) \\ G. C. Greubel, Dec 01 2017
(Magma) [(2*n-1)*(5*n^2-5*n+2)/2: n in [1..30]]; // G. C. Greubel, Dec 01 2017
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CROSSREFS
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1/12*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496.
Sequence in context: A039453 A342560 A219144 * A264850 A039408 A043231
Adjacent sequences: A063492 A063493 A063494 * A063496 A063497 A063498
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Aug 01 2001
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STATUS
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approved
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