%I #16 Oct 26 2022 03:04:55
%S 1,3,7,15,31,63,119,231,455,903,1799,3591,7175,14343,28679,57351,
%T 114695,229383,458759,917511,1835015,3670023,7340039,14680071,
%U 29360135,58720263,117440519,234881031,469762055,939524103,1879048199,3758096391
%N a(n) is the number whose binary representation is A138145(n).
%H G. C. Greubel, <a href="/A147596/b147596.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 (3,-2).
%F a(n) = 7*(2^(n-3) + 1) if n >= 6. - _Hagen von Eitzen_, Jun 02 2009
%F From _Colin Barker_, Sep 15 2013: (Start)
%F a(n) = 3*a(n-1) - 2*a(n-2), for n >= 8.
%F G.f.: x*(1-2*x^2)*(1+2*x^2+4*x^4) / ((1-x)*(1-2*x)). (End)
%F E.g.f.: (7/8)*(8*exp(x) + exp(2*x)) - (1/8)*(63 + 62*x + 30*x^2) - 7*x^3/6 - x^4/4 - x^5/30. - _G. C. Greubel_, Oct 25 2022
%t Join[{1,3,7,15,31}, 7*(1+2^(Range[6, 40] -3))] (* _G. C. Greubel_, Oct 25 2022 *)
%o (PARI) Vec(-x*(2*x^2-1)*(4*x^4+2*x^2+1)/((x-1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Sep 15 2013
%o (Magma) [1,3,7,15,31] cat [7*(1+2^(n-3)): n in [6..40]]; // _G. C. Greubel_, Oct 25 2022
%o (SageMath)
%o def A147596(n): return 7*(1+2^(n-3)) -(1/8)*(63*int(n==0) +62*int(n==1) +60*int(n ==2)) -(7*int(n==3) +6*int(n==4) +4*int(n==5))
%o [A147596(n) for n in range(1,40)] # _G. C. Greubel_, Oct 25 2022
%Y Cf. A138145, A145641, A147537, A147538, A147539.
%Y Cf. A147540, A147590, A147595, A147597.
%K base,easy,nonn
%O 1,2
%A _Omar E. Pol_, Nov 08 2008
%E More terms from _Hagen von Eitzen_, Jun 02 2009
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