A192834 Molecular topological indices of the Mycielski graphs.

0, 4, 80, 800, 6248, 43424, 283880, 1793600, 11110088, 68008544, 413290280, 2500208000, 15081582728, 90806120864, 546088834280, 3281497784000, 19708713860168, 118330793948384, 710297609395880, 4263033439001600, 25583180948198408, 153518974465539104

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Molecular Topological Index

Eric Weisstein's World of Mathematics, Mycielski Graph

Index entries for linear recurrences with constant coefficients, signature (16,-95,260,-324,144).

Formula

a(n) = (3*2^n - 8)*(18 - 27*2^n + 14*3^n)/36, n > 1, with a(1)=0.

G.f.: 4*x^2*(12*x^4 - 2*x^3 + 25*x^2 - 4*x - 1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)). - Colin Barker, Aug 07 2012

E.g.f.: (25 + 12*x - 144*exp(x) + 270*exp(2*x) - 112*exp(3*x) - 81*exp(4*x) + 42*exp(6*x))/36. - G. C. Greubel, Jan 04 2019

Maple

0, seq((3*2^n-8)*(18-27*2^n+14*3^n)/36, n=2..25); # Muniru A Asiru, Jan 05 2019

Mathematica

Table[If[n==1, 0, (3*2^n-8)*(18-27*2^n+14*3^n)/36], {n, 1, 30}]

Prog

(PARI) concat(0, Vec(4*x^2*(12*x^4-2*x^3+25*x^2-4*x-1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)) + O(x^30))) \\ Colin Barker, Oct 14 2017
(PARI) vector(30, n, if(n==1, 0, (3*2^n-8)*(18-27*2^n+14*3^n)/36)) \\ G. C. Greubel, Jan 04 2019
(Magma) [0] cat [(3*2^n-8)*(18-27*2^n+14*3^n)/36: n in [2..30]]; // G. C. Greubel, Jan 04 2019
(Sage) [0] + [(3*2^n-8)*(18-27*2^n+14*3^n)/36 for n in (2..30)] # G. C. Greubel, Jan 04 2019
(GAP) Concatenation([0], List([2..30], n -> (3*2^n-8)*(18-27*2^n+ 14*3^n)/36)); # G. C. Greubel, Jan 04 2019

Crossrefs

Cf. A122695.

Sequence in context: A345459 A366955 A269146 * A054322 A114488 A055787

Adjacent sequences: A192831 A192832 A192833 * A192835 A192836 A192837

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 11 2011

Status

approved