A192796 Molecular topological indices of the crown graphs.

0, 28, 132, 360, 760, 1380, 2268, 3472, 5040, 7020, 9460, 12408, 15912, 20020, 24780, 30240, 36448, 43452, 51300, 60040, 69720, 80388, 92092, 104880, 118800, 133900, 150228, 167832, 186760, 207060

Offset: 1

Author

Eric W. Weisstein, Jul 10 2011

Keywords

• nonn
• easy

Comments

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Crown Graph
• Eric Weisstein's World of Mathematics, Molecular Topological Index
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

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

Mathematica

CoefficientList[Series[4*x*(5*x+7)/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Jul 04 2012 *)
LinearRecurrence[{4,-6,4,-1},{0,28,132,360},30] (* Harvey P. Dale, Sep 04 2024 *)

PARI

a(n) = 2*n*(n-1)*(4*n-1) \\ Charles R Greathouse IV, Jul 10 2011

Formula

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

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

G.f.: 4*x^2*(5*x+7)/(1-x)^4. - Vincenzo Librandi, Jul 04 2012

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jul 04 2012