cp's OEIS Frontend

A297928 a(n) = 2*4^n + 3*2^n - 1.

%I A297928 #9 Apr 22 2018 08:26:18
%S A297928 4,13,43,151,559,2143,8383,33151,131839,525823,2100223,8394751,
%T A297928 33566719,134242303,536920063,2147581951,8590131199,34360131583,
%U A297928 137439739903,549757386751,2199026401279,8796099313663,35184384671743,140737513521151,562950003752959,2251799914348543
%N A297928 a(n) = 2*4^n + 3*2^n - 1.
%C A297928 For n > 0, in binary, this is a 1 followed by n-1 0's followed by 10 followed by n 1's.
%H A297928 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8)
%F A297928 G.f.: (4 - 15*x + 8*x^2)/((1 - x)*(1 - 2*x)*(1 - 4*x)).
%F A297928 E.g.f.: 2*e^(4*x) + 3*e^(2*x) - e^x.
%F A297928 a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3), n > 2.
%F A297928 a(n) = A000918(n) + A085601(n).
%e A297928 a(0) = 2*4^0 + 3*2^0 - 1 = 4;   in binary, 100.
%e A297928 a(1) = 2*4^1 + 3*2^1 - 1 = 13;  in binary, 1101.
%e A297928 a(2) = 2*4^2 + 3*2^2 - 1 = 43;  in binary, 101011.
%e A297928 a(3) = 2*4^3 + 3*2^3 - 1 = 151; in binary, 10010111.
%e A297928 a(4) = 2*4^4 + 3*2^4 - 1 = 559; in binary, 1000101111.
%e A297928 ...
%t A297928 Table[2 4^n+3 2^n-1,{n,0,30}] (* or *) LinearRecurrence[{7,-14,8},{4,13,43},30] (* _Harvey P. Dale_, Apr 22 2018 *)
%o A297928 (PARI) a(n) = 2*4^n + 3*2^n - 1
%o A297928 (PARI) first(n) = Vec((4 - 15*x + 8*x^2)/((1 - x)*(1 - 2*x)*(1 - 4*x)) + O(x^n))
%Y A297928 A lower bound for A296807.
%Y A297928 Cf. A000918, A085601.
%K A297928 nonn,easy
%O A297928 0,1
%A A297928 _Iain Fox_, Jan 08 2018