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A063494 a(n) = (2*n - 1)*(7*n^2 - 7*n + 3)/3. 19

%I

%S 1,17,75,203,429,781,1287,1975,2873,4009,5411,7107,9125,11493,14239,

%T 17391,20977,25025,29563,34619,40221,46397,53175,60583,68649,77401,

%U 86867,97075,108053,119829,132431,145887,160225,175473,191659,208811

%N a(n) = (2*n - 1)*(7*n^2 - 7*n + 3)/3.

%C Interpret A176271 as an infinite square array read by antidiagonals, with rows 1,5,11,19,...; 3,9,17,27,... and so on. The sum of the terms in the n X n upper submatrix are s(n) = 1, 18, 93, 296, ... = n^2*(7*n^2-1)/6, and a(n) = s(n) - s(n-1) are the first differences. - _J. M. Bergot_, Jun 27 2013

%H Harry J. Smith, <a href="/A063494/b063494.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. Rep., 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+12*x+x^2)/(1-x)^4. - _Colin Barker_, Mar 02 2012

%F E.g.f.: (-3 + 6*x + 21*x^2 + 14*x^3)*exp(x)/3 + 1. - _G. C. Greubel_, Dec 01 2017

%t Table[(2*n - 1)*(7*n^2 - 7*n + 3)/3, {n,1,30}] (* or *) LinearRecurrence[{4,-6,4,-1}, {1,17,75,203}, 30] (* _G. C. Greubel_, Dec 01 2017 *)

%o (PARI) { for (n=1, 1000, write("b063494.txt", n, " ", (2*n - 1)*(7*n^2 - 7*n + 3)/3) ) } \\ _Harry J. Smith_, Aug 23 2009

%o (MAGMA) [(2*n - 1)*(7*n^2 - 7*n + 3)/3: n in [1..30]]; // _G. C. Greubel_, Dec 01 2017

%o (PARI) x='x+O('x^30); Vec(serlaplace((-3+6*x+21*x^2+14*x^3)*exp(x)/3 + 1)) \\ _G. C. Greubel_, Dec 01 2017

%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 October 21 12:52 EDT 2018. Contains 316422 sequences. (Running on oeis4.)