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a(n) = n*(7*n^2-4)/3.
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%I #26 Sep 01 2017 15:12:17

%S 0,1,16,59,144,285,496,791,1184,1689,2320,3091,4016,5109,6384,7855,

%T 9536,11441,13584,15979,18640,21581,24816,28359,32224,36425,40976,

%U 45891,51184,56869,62960,69471,76416,83809,91664,99995,108816,118141

%N a(n) = n*(7*n^2-4)/3.

%C Also as a(n)=(1/6)*(14*n^3-8*n), n>0: structured heptagonal anti-diamond numbers (vertex structure 15) (Cf. A100186 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov 07 2004

%H Harry J. Smith, <a href="/A063521/b063521.txt">Table of n, a(n) for n = 0..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. (11).

%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+12*x+x^2)/(1-x)^4. - _Colin Barker_, Jan 10 2012

%F E.g.f.: (x/3)*(3 + 21*x + 7*x^2)*exp(x). - _G. C. Greubel_, Sep 01 2017

%p A063521:=n->n*(7*n^2-4)/3; seq(A063521(k), k=0..100); # _Wesley Ivan Hurt_, Oct 24 2013

%t lst={};Do[AppendTo[lst, n*(7*n^2-4)/3], {n, 1, 6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 02 2008 *)

%t CoefficientList[Series[x*(1+12*x+x^2)/(1-x)^4, {x, 0, 50}], x] (* _G. C. Greubel_, Sep 01 2017 *)

%o (PARI) { for (n=0, 1000, write("b063521.txt", n, " ", n*(7*n^2 - 4)/3) ) } \\ _Harry J. Smith_, Aug 25 2009

%Y 1/12*t*(n^3-n)+n for t = 2, 4, 6, ... gives A004006, A006527, A006003, A005900, A004068, A000578, A004126, A000447, A004188, A004466, A004467, A007588, A062025, A063521, A063522, A063523.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Aug 02 2001