|
%I #19 Oct 25 2022 16:49:28
%S 1,7,31,119,455,1799,7175,28679,114695,458759,1835015,7340039,
%T 29360135,117440519,469762055,1879048199,7516192775,30064771079,
%U 120259084295,481036337159,1924145348615,7696581394439,30786325577735,123145302310919,492581209243655
%N a(n) is the number whose binary representation is A138146(n).
%C Bisection of A147596.
%H Colin Barker, <a href="/A147597/b147597.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F From _R. J. Mathar_, Feb 05 2010: (Start)
%F a(n) = 5*a(n-1) - 4*a(n-2) for n>5.
%F G.f.: x*(2*x+1)*(2*x-1)*(4*x^2+2*x+1)/((4*x-1)*(1-x)). (End)
%F a(n) = 7*4^(n-2) + 7 for n>3. - _Colin Barker_, Nov 25 2016
%F E.g.f.: (7/16)*(16*exp(x) + exp(4*x)) -(119/16) -31*x/4 -7*x^2/2 -2*x^3/3. - _G. C. Greubel_, Oct 25 2022
%t Table[FromDigits[#, 2] &@ If[n < 4, ConstantArray[1, 2 n - 1], Join[#, ConstantArray[0, 2 n - 7], #]] &@ ConstantArray[1, 3], {n, 25}] (* or *)
%t Rest@ CoefficientList[Series[x (2 x + 1) (2 x - 1) (4 x^2 + 2 x + 1)/((4 x - 1) (1 - x)), {x, 0, 25}], x] (* _Michael De Vlieger_, Nov 25 2016 *)
%o (PARI) Vec(x*(2*x+1)*(2*x-1)*(4*x^2+2*x+1)/((4*x-1)*(1-x)) + O(x^30)) \\ _Colin Barker_, Nov 25 2016
%o (Magma) [1,7,31] cat [7*(1+4^(n-2)): n in [4..40]]; // _G. C. Greubel_, Oct 25 2022
%o (SageMath)
%o def A147597(n): return 7*(1+4^(n-2)) -(119/16)*int(n==0) -(31/4)*int(n==1) -7*int(n==2) -4*int(n==3)
%o [A147597(n) for n in range(1,41)] # _G. C. Greubel_, Oct 25 2022
%Y Cf. A138146, A145641, A147537, A147538, A147539.
%Y Cf. A147540, A147590, A147595, A147596.
%K base,easy,nonn
%O 1,2
%A _Omar E. Pol_, Nov 08 2008
%E More terms from _R. J. Mathar_, Feb 05 2010
|
