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

Author

Eric W. Weisstein, Jul 11 2011

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A090197.

Programs

GAP

List([1..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

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 *)

PARI

vector(40, n, 4*n*(-3+3*n+n^2)) \\ G. C. Greubel, Jan 05 2019

Sage

[4*n*(-3+3*n+n^2) for n in (1..40)] # G. C. Greubel, Jan 05 2019

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