A016173 Expansion of 1/((1-6*x)*(1-10*x)).

1, 16, 196, 2176, 23056, 238336, 2430016, 24580096, 247480576, 2484883456, 24909300736, 249455804416, 2496734826496, 24980408958976, 249882453753856, 2499294722523136, 24995768335138816, 249974610010832896, 2499847660064997376, 24999085960389984256, 249994515762339905536, 2499967094574039433216

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..990
• Index entries for linear recurrences with constant coefficients, signature (16,-60).

Crossrefs

Cf. A016129.

Programs

Magma

[(10^(n+1) - 6^(n+1))/4: n in [0..40]]; // G. C. Greubel, Nov 13 2024

Mathematica

Table[(10^(n+1) - 6^(n+1))/4, {n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)
CoefficientList[Series[1/((1-6x)(1-10x)), {x,0,40}], x]  (* Harvey P. Dale, Mar 12 2011 *)

Python

def A016173(n): return (pow(10,n+1) - pow(6,n+1))//4
print([A016173(n) for n in range(41)]) # G. C. Greubel, Nov 13 2024

Formula

a(n) = (10^(n+1) - 6^(n+1))/4. - Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008

a(n) = 16*a(n-1) - 60*a(n-2). - Philippe Deléham, Jan 01 2009

a(n) = 10*a(n-1) + 6^n, a(0)=1. - Vincenzo Librandi, Feb 09 2011

E.g.f.: (1/2)*(5*exp(10*x) - 3*exp(6*x)). - G. C. Greubel, Nov 13 2024

Extensions

More terms added by G. C. Greubel, Nov 13 2024