A016174 Expansion of 1/((1-6*x)*(1-11*x)).

1, 17, 223, 2669, 30655, 344981, 3841447, 42535853, 469573999, 5175391685, 56989774711, 627250318877, 6901930289983, 75934293883829, 835355596886215, 9189381750732941, 101086020367969807, 1111963150707112613, 12231696217734907159, 134549267754823989245, 1480045601461503944671, 16280523553027183769237

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..955
• Index entries for linear recurrences with constant coefficients, signature (17,-66).

Crossrefs

Cf. A016129.

Programs

Magma

[(11^(n+1) - 6^(n+1))/5: n in [0..40]]; // G. C. Greubel, Nov 13 2024

Maple

A016174:=n->(11^(n + 1) - 6^(n + 1))/5; seq(A016174(n), n=0..30); # Wesley Ivan Hurt, Jan 30 2014

Mathematica

Table[(11^(n+1) -6^(n+1))/5, {n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)
LinearRecurrence[{17, -66}, {1, 17}, 41] (* G. C. Greubel, Nov 13 2024 *)

PARI

Vec(1/((1-6*x)*(1-11*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

SageMath

A016174=BinaryRecurrenceSequence(17,-66,1,17)
print([A016174(n) for n in range(41)]) # G. C. Greubel, Nov 13 2024

Formula

a(n) = (11^(n+1) - 6^(n+1))/5. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 06 2005

a(n) = 11*a(n-1) + 6^n, a(0)=1. - Vincenzo Librandi, Feb 09 2011

E.g.f.: (1/5)*(11*exp(11*x) - 6*exp(6*x)). - G. C. Greubel, Nov 13 2024

Extensions

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