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A063492
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a(n) = (2*n - 1)*(11*n^2 - 11*n + 6)/6.
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18
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1, 14, 60, 161, 339, 616, 1014, 1555, 2261, 3154, 4256, 5589, 7175, 9036, 11194, 13671, 16489, 19670, 23236, 27209, 31611, 36464, 41790, 47611, 53949, 60826, 68264, 76285, 84911, 94164, 104066, 114639, 125905, 137886, 150604, 164081, 178339, 193400, 209286, 226019
(list;
graph;
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listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (10).
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FORMULA
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G.f.: x*(1+x)*(1 + 9*x + x^2)/(1-x)^4. - Colin Barker, Apr 24 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. - Wesley Ivan Hurt, Dec 16 2015
E.g.f.: (-6 + 12*x + 33*x^2 + 22*x^3)*exp(x)/6 + 1. - G. C. Greubel, Dec 01 2017
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MAPLE
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {1, 14, 60, 161}, 40] (* Vincenzo Librandi, Dec 16 2015 *)
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PROG
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(PARI) { for (n=1, 1000, write("b063492.txt", n, " ", (2*n - 1)*(11*n^2 - 11*n + 6)/6) ) } \\ Harry J. Smith, Aug 23 2009
(PARI) Vec(x*(1+x)*(1+9*x+x^2)/(1-x)^4 + O(x^100)) \\ Altug Alkan, Dec 16 2015
(Python)
A063492_list, m = [], [22, -11, 2, 1]
for _ in range(10**2):
for i in range(3):
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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.
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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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