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A257548 a(1) = 1, a(2) = 2, a(3) = 5, a(4) = 8 and a(5) = 15, a(n) = Sum_{j=1..n-1} a(j).

%I A257548 #42 Jan 05 2023 03:13:29
%S A257548 1,2,5,8,15,31,62,124,248,496,992,1984,3968,7936,15872,31744,63488,
%T A257548 126976,253952,507904,1015808,2031616,4063232,8126464,16252928,
%U A257548 32505856,65011712,130023424,260046848,520093696,1040187392,2080374784,4160749568,8321499136
%N A257548 a(1) = 1, a(2) = 2, a(3) = 5, a(4) = 8 and a(5) = 15, a(n) = Sum_{j=1..n-1} a(j).
%C A257548 31 is the only prime after 5 (the remaining terms are even).
%H A257548 G. C. Greubel, <a href="/A257548/b257548.txt">Table of n, a(n) for n = 1..1000</a>
%H A257548 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F A257548 For n>=6, a(n) = 31*2^(n-6).
%F A257548 For n>=6, a(n) = A206371(n-6) - 1.
%F A257548 G.f.: x*(1+x^2-2*x^3-x^4+x^5)/(1-2*x). - _Robert G. Wilson v_, May 05 2015
%F A257548 E.g.f.: (31/64)*exp(2*x) + x/32 + x^2/32 + 3*x^3/16 + x^4/96 - x^5/240. - _G. C. Greubel_, Jan 05 2023
%t A257548 Join[{1,2,5,8,15}, Table[31*2^(n-6), {n,6,50}]] (* _Vincenzo Librandi_, May 03 2015 *)
%t A257548 CoefficientList[ Series[(x^5 -x^4 -2x^3 +x^2 +1)/(1 -2x), {x, 0, 33}], x] (* _Robert G. Wilson v_, May 05 2015 *)
%t A257548 Join[{1,2,5,8,15},NestList[2#&,31,30]] (* _Harvey P. Dale_, Oct 09 2018 *)
%o A257548 (Magma) [1,2,5,8] cat [31*2^n div 64: n in [5..50]]; // _Vincenzo Librandi_, May 03 2015
%o A257548 (SageMath)
%o A257548 def A257548(n): return (4*fibonacci(n+1) -3 -(-1)^n)/2 if (n<6) else 31*2^(n-6)
%o A257548 [A257548(n) for n in range(1,51)] # _G. C. Greubel_, Jan 05 2023
%Y A257548 Cf. A206371.
%K A257548 nonn,easy
%O A257548 1,2
%A A257548 _Giovanni Teofilatto_, Apr 29 2015