A016241 Expansion of 1/((1-x)*(1-6*x)*(1-7*x)).
1, 14, 141, 1246, 10277, 81270, 624877, 4710062, 34985973, 256995046, 1871524733, 13536029598, 97364345989, 697223254742, 4974599780109, 35386420442254, 251090274984725, 1777943916226758, 12567479361589405, 88703587219138430, 625312500662044581
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (14,-55,42).
Programs
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Magma
[(1 -6^(n+2) +5*7^(n+1))/30 : n in [0..40]]; // G. C. Greubel, Jan 30 2022
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Mathematica
Table[(1 -6^(n+2) +5*7^(n+1))/30, {n, 40}] (* or *) CoefficientList[Series[1/((1-z)(1-6*z)(1-7*z)), {z, 0, 40}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *) LinearRecurrence[{14,-55,42},{1,14,141},40] (* Harvey P. Dale, Aug 05 2011 *) -
PARI
Vec(1/((1-x)*(1-6*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
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Sage
[(1 -6^(n+2) +5*7^(n+1))/30 for n in (0..40)] # G. C. Greubel, Jan 30 2022
Formula
a(0)=1, a(1)=14, a(n) = 13*a(n-1) - 42*a(n-2) + 1. - Vincenzo Librandi, Feb 10 2011
a(n) = (1 - 6^(n+2) + 5*7^(n+1))/30. - Vladimir Joseph Stephan Orlovsky, Jul 21 2011
a(0)=1, a(1)=14, a(2)=141, a(n) = 14*a(n-1) - 55*a(n-2) + 42*a(n-3). - Harvey P. Dale, Aug 05 2011
E.g.f.: (1/30)*(exp(x) - 36*exp(6*x) + 35*exp(7*x)). - G. C. Greubel, Jan 30 2022