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%I #46 Mar 04 2022 19:05:12
%S 1,8,45,220,1001,4368,18565,77540,320001,1309528,5326685,21572460,
%T 87087001,350739488,1410132405,5662052980,22712782001,91044838248,
%U 364760483725,1460785327100,5848371485001,23409176469808,93683777468645,374876324642820,1499928942876001
%N Expansion of 1/((1-x)*(1-3*x)*(1-4*x)).
%C Binomial transform of A085277. - _Paul Barry_, Jun 25 2003
%C Number of walks of length 2n+5 between two nodes at distance 5 in the cycle graph C_12. - _Herbert Kociemba_, Jul 05 2004
%H Muniru A Asiru, <a href="/A016208/b016208.txt">Table of n, a(n) for n = 0..1000</a>
%H Natalia Agudelo Muñetón, Agustín Moreno Cañadas, Pedro Fernando Fernández Espinosa, and Isaías David Marín Gaviria, <a href="https://doi.org/10.3390/math9233042">Brauer Configuration Algebras and Their Applications in Graph Energy Theory</a>, Mathematics (2021) Vol. 9, 3042.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-19,12)
%F a(n) = 16*4^n/3 + 1/6 - 9*3^n/2. - _Paul Barry_, Jun 25 2003
%F a(0) = 0, a(1) = 8, a(n) = 7*a(n-1) - 12*a(n-2) + 1. - _Vincenzo Librandi_, Feb 10 2011
%F a(0) = 1, a(1) = 8, a(2) = 45, a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3). - _Harvey P. Dale_, Apr 09 2012
%t Table[(2^(2*n + 3) - 3^(n + 2) + 1)/6, {n, 40}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 19 2011 *)
%t CoefficientList[Series[1/((1-x)(1-3x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[ {8,-19,12},{1,8,45},30] (* _Harvey P. Dale_, Apr 09 2012 *)
%o (PARI) Vec(1/((1-x)*(1-3*x)*(1-4*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 23 2012
%o (GAP) a:=[1,8,45];; for n in [4..30] do a[n]:=8*a[n-1]-19*a[n-2]+12*a[n-3]; od; Print(a); # _Muniru A Asiru_, Apr 19 2019
%Y Cf. A000225, A000295, A000392, A002275, A003462, A003463, A003464, A023000, A023001, A002452, A016123, A016125, A016256.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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