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

1,2

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).

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

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 *)

Prog

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

Crossrefs

Sequence in context: A318778 A184679 A123376 * A124956 A014705 A126415

Adjacent sequences: A192793 A192794 A192795 * A192797 A192798 A192799

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 10 2011

Status

approved