%I #24 Feb 29 2024 15:50:13

%S 1,4,16,64,257,1028,4112,16448,65793,263172,1052688,4210752,16843009,

%T 67372036,269488144,1077952576,4311810305,17247241220,68988964880,

%U 275955859520,1103823438081,4415293752324,17661175009296,70644700037184

%N Expansion of 1/((1-4*x)*(1-x^4)).

%H G. C. Greubel, <a href="/A083589/b083589.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,0,1,-4)

%F a(0)=1, a(n) = 4*a(n-1) if n is not a multiple of 4, otherwise a(n) = 4*a(n-1) + 1. - _Vincenzo Librandi_, Mar 19 2011

%F a(n) = 4^(n+4)/255 -1/12 +(-1)^n/20 +(-1)^floor(n/2)*A010685(n)/34. - _R. J. Mathar_, Mar 19 2011

%F a(0)=1, a(1)=4, a(2)=16, a(3)=64, a(4)=257, a(n) = 4*a(n-1) + a(n-4) - 4*a(n-5). - _Harvey P. Dale_, Sep 13 2011

%F a(n) = floor(64*(2^(2*(n+1))+1)/255). - _Tani Akinari_, Jul 09 2013

%t CoefficientList[Series[1/((1-4x)(1-x^4)),{x,0,30}],x] (* or *) LinearRecurrence[ {4,0,0,1,-4},{1,4,16,64,257},31] (* _Harvey P. Dale_, Sep 13 2011 *)

%o (PARI) a(n)=(4^(n+4)+64)\255 \\ _Charles R Greathouse IV_, Jul 09 2013

%Y Cf. A033139, A000975.

%K easy,nonn

%O 0,2

%A _Paul Barry_, May 02 2003