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A120723 Expansion of x*(1+3*x)*(1+6*x+16*x^2)/((1-x)*(1+2*x)*(1-3*x-2*x^2)). 1

%I #23 Jul 20 2023 11:16:24

%S 1,11,63,247,887,3207,11383,40679,144663,515719,1835831,6540327,

%T 23289943,82955975,295436919,1052244583,3747563927,13347268359,

%U 47536758199,169305160871,602988299991,2147576619847,7648703663351

%N Expansion of x*(1+3*x)*(1+6*x+16*x^2)/((1-x)*(1+2*x)*(1-3*x-2*x^2)).

%H G. C. Greubel, <a href="/A120723/b120723.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,7,-4,-4).

%F G.f.: x*(1+3*x)*(1+6*x+16*x^2)/((1-x)*(1+2*x)*(1-3*x-2*x^2)). - _Colin Barker_, Apr 04 2012

%F a(n) = 12*[n=0] - 23/3 + (-2)^n/6 - (9/2)*(A007482(n) - 5*A007482(n- 1)). - _G. C. Greubel_, Jul 20 2023

%t CoefficientList[Series[(1+3x)*(1 +6x +16x^2)/((1-x)*(1+2x)*(1-3x-2x^2)), {x, 0, 50}], x] (* _Bruno Berselli_, Apr 04 2012 *)

%t LinearRecurrence[{2,7,-4,-4}, {1,11,63,247}, 40] (* _G. C. Greubel_, Jul 20 2023 *)

%o (Magma) I:=[1,11,63,247]; [n le 4 select I[n] else 2*Self(n-1) + 7*Self(n-2) -4*Self(n-3) -4*Self(n-4): n in [1..40]]; // _G. C. Greubel_, Jul 20 2023

%o (SageMath)

%o A007482=BinaryRecurrenceSequence(3,2,1,3)

%o def A120723(n): return 12*int(n==0) - (1/6)*(46 - (-2)^n + 27*(A007482(n) - 5*A007482(n-1)))

%o [A120723(n) for n in range(41)] # _G. C. Greubel_, Jul 20 2023

%Y Cf. A007482.

%K nonn,easy

%O 1,2

%A _Roger L. Bagula_, Aug 17 2006

%E Edited by _N. J. A. Sloane_, Jun 15 2007

%E Meaningful name from _Joerg Arndt_, Dec 26 2022

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)