cp's OEIS Frontend

A063521 a(n) = n*(7*n^2-4)/3.

%I A063521 #30 Dec 28 2024 11:45:28
%S A063521 0,1,16,59,144,285,496,791,1184,1689,2320,3091,4016,5109,6384,7855,
%T A063521 9536,11441,13584,15979,18640,21581,24816,28359,32224,36425,40976,
%U A063521 45891,51184,56869,62960,69471,76416,83809,91664,99995,108816,118141,127984,138359,149280,160761
%N A063521 a(n) = n*(7*n^2-4)/3.
%C A063521 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 A063521 Harry J. Smith, <a href="/A063521/b063521.txt">Table of n, a(n) for n = 0..1000</a>
%H A063521 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 A063521 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
%F A063521 G.f.: x*(1+12*x+x^2)/(1-x)^4. - _Colin Barker_, Jan 10 2012
%F A063521 E.g.f.: (x/3)*(3 + 21*x + 7*x^2)*exp(x). - _G. C. Greubel_, Sep 01 2017
%p A063521 A063521:=n->n*(7*n^2-4)/3; seq(A063521(k), k=0..100); # _Wesley Ivan Hurt_, Oct 24 2013
%t A063521 lst={};Do[AppendTo[lst, n*(7*n^2-4)/3], {n, 1, 6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 02 2008 *)
%t A063521 CoefficientList[Series[x*(1+12*x+x^2)/(1-x)^4, {x, 0, 50}], x] (* _G. C. Greubel_, Sep 01 2017 *)
%o A063521 (PARI) a(n) = { n*(7*n^2 - 4)/3 } \\ _Harry J. Smith_, Aug 25 2009
%Y A063521 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 A063521 nonn,easy
%O A063521 0,3
%A A063521 _N. J. A. Sloane_, Aug 02 2001