A192796 - OEIS

%I #22 Sep 04 2024 15:31:55

%S 0,28,132,360,760,1380,2268,3472,5040,7020,9460,12408,15912,20020,

%T 24780,30240,36448,43452,51300,60040,69720,80388,92092,104880,118800,

%U 133900,150228,167832,186760,207060

%N Molecular topological indices of the crown graphs

%C Crown graphs are defined for n>=3; extended to n=1 using the closed form.

%H Charles R Greathouse IV, <a href="/A192796/b192796.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CrownGraph.html">Crown Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>

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

%F a(n) = 2*(n-1)*n*(4*n-1).

%F a(n) = 4*A051895(n).

%F G.f.: 4*x^2*(5*x+7)/(1-x)^4. - _Vincenzo Librandi_, Jul 04 2012

%F a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - _Vincenzo Librandi_, Jul 04 2012

%t CoefficientList[Series[4*x*(5*x+7)/(1-x)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jul 04 2012 *)

%t LinearRecurrence[{4,-6,4,-1},{0,28,132,360},30] (* _Harvey P. Dale_, Sep 04 2024 *)

%o (PARI) a(n) = 2*n*(n-1)*(4*n-1) \\ _Charles R Greathouse IV_, Jul 10 2011

%o (Magma)  I:=[0, 28, 132, 360]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jul 04 2012

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Jul 10 2011