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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 10 2011
STATUS
approved