A181685 Expansion of 36*x^2*(1+6*x-36*x^2) / ( (1-6*x)^2 *(1+6*x+36*x^2) ).

0, 36, 432, 1296, 15552, 139968, 559872, 5038848, 40310784, 181398528, 1451188224, 10883911680, 52242776064, 391820820480, 2821109907456, 14105549537280, 101559956668416, 710919696678912, 3656158440062976, 25593109080440832, 175495605123022848, 921351926895869952

Offset: 1

Author

Florentin Smarandache (smarand(AT)unm.edu), Nov 04 2010

Keywords

• nonn
• easy

Comments

The old definition was: Colorless combinations of quarks and antiquarks of length n >= 1.

References

• Florentin Smarandache, "Matter, Antimatter and Unmatter", Infinite Energy, Concord, NH, USA, Vol. 11, Issue 62, 50-51, 2005.

Links

• Florentin Smarandache, A New Form of Matter - Unmatter, Formed by Particles and Anti-Particles", EXT-2004-182 in CERN's web site, 2004.
• Index entries for linear recurrences with constant coefficients, signature (6,0,216,-1296).

Programs

Mathematica

Table[(n - 1 - 2 Floor[(n - 1)/3]) 6^n, {n, 1, 30}]
LinearRecurrence[{6,0,216,-1296},{0,36,432,1296},30] (* Harvey P. Dale, Jul 04 2019 *)

PARI

concat(0, 36*Vec(x*(1+6*x-36*x^2) / (1-6*x)^2 / (1+6*x+36*x^2)+O(x^99)))

Formula

a(n) = ( n - 1 - 2*floor((n-1)/3) )*6^n.

Extensions

Entry revised by Editors of the OEIS, Sep 11 2014