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A063493 a(n) = (2*n-1)*(13*n^2-13*n+6)/6. 17

%I

%S 1,16,70,189,399,726,1196,1835,2669,3724,5026,6601,8475,10674,13224,

%T 16151,19481,23240,27454,32149,37351,43086,49380,56259,63749,71876,

%U 80666,90145,100339,111274,122976,135471,148785,162944,177974,193901

%N a(n) = (2*n-1)*(13*n^2-13*n+6)/6.

%H Harry J. Smith, <a href="/A063493/b063493.txt">Table of n, a(n) for n = 1..1000</a>

%H T. P. Martin, <a href="http://dx.doi.org/10.1016/0370-1573(95)00083-6">Shells of atoms</a>, Phys. Reports, 273 (1996), 199-241, eq. (10).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F G.f.: x*(1+x)*(1+11*x+x^2)/(1-x)^4. - _Colin Barker_, Apr 20 2012

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - _Vincenzo Librandi_, Dec 16 2015

%F E.g.f.: (-6 + 12*x + 39*x^2 + 26*x^3)*exp(x)/6 + 1. - _G. C. Greubel_, Dec 01 2017

%t Table[(2 n - 1) (13 n^2 - 13 n + 6)/6, {n, 1, 40}] (* _Bruno Berselli_, Dec 16 2015 *)

%t LinearRecurrence[{4,-6,4,-1}, {1,16,70,189}, 30] (* _G. C. Greubel_, Dec 01 2017 *)

%o (PARI) { for (n=1, 1000, write("b063493.txt", n, " ", (2*n - 1)*(13*n^2 - 13*n + 6)/6) ) } \\ _Harry J. Smith_, Aug 23 2009

%o (PARI) x='x+O('x^30); Vec(serlaplace((-6+12*x+39*x^2+26*x^3)*exp(x)/6 + 1)) \\ _G. C. Greubel_, Dec 01 2017

%o (Python)

%o A063493_list, m = [], [26, -13, 2, 1]

%o for _ in range(10**2):

%o A063493_list.append(m[-1])

%o for i in range(3):

%o m[i+1] += m[i] # _Chai Wah Wu_, Dec 15 2015

%o (MAGMA) [(2*n-1)*(13*n^2-13*n+6)/6: n in [1..40]]; // _Vincenzo Librandi_, Dec 16 2015

%Y 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.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Aug 01 2001

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Last modified February 24 18:24 EST 2018. Contains 299628 sequences. (Running on oeis4.)