A192845 Molecular topological indices of the sun graphs.

4, 56, 180, 400, 740, 1224, 1876, 2720, 3780, 5080, 6644, 8496, 10660, 13160, 16020, 19264, 22916, 27000, 31540, 36560, 42084, 48136, 54740, 61920, 69700, 78104, 87156, 96880, 107300, 118440

Offset

1,1

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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) = 4*n*(-3 + 3*n + n^2).

a(n) = 4*A090197(n).

G.f.: 4*x*(1 + 10*x - 5*x^2)/(1-x)^4. - Colin Barker, Aug 07 2012

E.g.f.: 4*x*(1 + 6*x + x^2)*exp(x). - G. C. Greubel, Jan 05 2019

Mathematica

Table[4*n*(-3+3*n+n^2), {n, 1, 40}] (* G. C. Greubel, Jan 05 2019 *)
LinearRecurrence[{4, -6, 4, -1}, {4, 56, 180, 400}, 30] (* Harvey P. Dale, Mar 02 2024 *)

Prog

(PARI) vector(40, n, 4*n*(-3+3*n+n^2)) \\ G. C. Greubel, Jan 05 2019
(Magma) [4*n*(-3+3*n+n^2): n in [1..40]]; // G. C. Greubel, Jan 05 2019
(SageMath) [4*n*(-3+3*n+n^2) for n in (1..40)] # G. C. Greubel, Jan 05 2019
(GAP) List([1..40], n -> 4*n*(-3+3*n+n^2)); # G. C. Greubel, Jan 05 2019

Crossrefs

Cf. A090197.

Sequence in context: A168133 A189864 A360262 * A144138 A331776 A006592

Adjacent sequences: A192842 A192843 A192844 * A192846 A192847 A192848

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 11 2011

Status

approved