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Expansion of 1/((1-5*x)*(1-12*x)).
2

%I #32 Nov 10 2024 02:29:52

%S 1,17,229,2873,35101,424337,5107669,61370153,736832461,8843942657,

%T 106137077509,1273693758233,15284569239421,183416051576177,

%U 2200998722429749,26412015186735113,316944334828711981,3803332780883996897,45639997185305228389,547679985297149068793

%N Expansion of 1/((1-5*x)*(1-12*x)).

%H G. C. Greubel, <a href="/A016166/b016166.txt">Table of n, a(n) for n = 0..920</a>

%H Daniele A. Gewurz and Francesca Merola, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Gewurz/gewurz5.html">Sequences realized as Parker vectors of oligomorphic permutation groups</a>, J. Integer Seqs., Vol. 6, 2003.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-60).

%F G.f.: 1/((1-5*x)*(1-12*x)).

%F a(n) = (12^(n+1) - 5^(n+1))/7. - _Bruno Berselli_, Feb 09 2011

%F a(n) = 12*a(n-1) + 5^n, a(0)=1. - _Vincenzo Librandi_, Feb 09 2011

%F a(n) = 17*a(n-1) - 60*a(n-2), n > 1. - _Wesley Ivan Hurt_, Aug 28 2015

%F E.g.f.: (1/7)*(12*exp(12*x) - 5*exp(5*x)). - _G. C. Greubel_, Nov 10 2024

%p A016166:=n->(12^(n+1)-5^(n+1))/7: seq(A016166(n), n=0..30); # _Wesley Ivan Hurt_, Aug 28 2015

%t LinearRecurrence[{17,-60}, {1,17}, 41] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2011 *)

%t Table[(12^(n+1)-5^(n+1))/7, {n,0,40}] (* _Wesley Ivan Hurt_, Aug 28 2015 *)

%o (Magma) [(12^(n+1)-5^(n+1))/7 : n in [0..30]]; // _Wesley Ivan Hurt_, Aug 28 2015

%o (SageMath)

%o A016166=BinaryRecurrenceSequence(17,-60,1,17)

%o [A016166(n) for n in range(41)] # _G. C. Greubel_, Nov 10 2024

%Y Cf. A016161.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_