cp's OEIS Frontend

A088556 Numbers of the form (4^n + 4^(n-1) + ... + 1) + (n mod 2).

%I A088556 #28 Jan 12 2025 09:21:33
%S A088556 6,21,86,341,1366,5461,21846,87381,349526,1398101,5592406,22369621,
%T A088556 89478486,357913941,1431655766,5726623061,22906492246,91625968981,
%U A088556 366503875926,1466015503701,5864062014806,23456248059221,93824992236886,375299968947541,1501199875790166
%N A088556 Numbers of the form (4^n + 4^(n-1) + ... + 1) + (n mod 2).
%H A088556 Colin Barker, <a href="/A088556/b088556.txt">Table of n, a(n) for n = 1..1000</a>
%H A088556 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,1,-4).
%F A088556 If n is even, then 4^n + ... + 1 = (4^(n+1) - 1)/3 = (2^(n+1) - 1)*(2^(n+1) + 1)/3. - _R. K. Guy_, Nov 17 2003
%F A088556 a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3). - _Colin Barker_, Apr 02 2012
%F A088556 G.f.: x*(6-3*x-4*x^2) / ((1-x)*(1+x)*(1-4*x)). - _Colin Barker_, Apr 02 2012
%t A088556 LinearRecurrence[{4, 1, -4}, {6, 21, 86}, 50] (* _Vincenzo Librandi_, Jun 14 2015 *)
%o A088556 (PARI) trajpolypn(n1) = { for(x1=1,n1, y1 = polypn(4,x1); print1(y1",") ) }
%o A088556 polypn(n,p) = { x=n; if(p%2,y=2,y=1); for(m=1,p, y=y+x^m; ); return(y) }
%o A088556 (PARI) Vec(x*(6-3*x-4*x^2)/((1-x)*(1+x)*(1-4*x)) + O(x^30)) \\ _Colin Barker_, Jun 13 2015
%o A088556 (Magma) I:=[6,21,86]; [n le 3 select I[n] else 4*Self(n-1)+Self(n-2)-4*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 14 2015
%Y A088556 Cf. A002450, A047849.
%K A088556 nonn,easy
%O A088556 1,1
%A A088556 _Cino Hilliard_, Nov 17 2003