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A047393 Numbers that are congruent to {0, 1} mod 8.

%I A047393 #62 Jul 02 2025 16:01:57
%S A047393 0,1,8,9,16,17,24,25,32,33,40,41,48,49,56,57,64,65,72,73,80,81,88,89,
%T A047393 96,97,104,105,112,113,120,121,128,129,136,137,144,145,152,153,160,
%U A047393 161,168,169,176,177,184,185,192,193,200,201,208,209,216,217,224,225,232
%N A047393 Numbers that are congruent to {0, 1} mod 8.
%C A047393 Numbers k such that floor(k/2) = 4*floor(k/8). - _Bruno Berselli_, Oct 05 2017
%H A047393 David Lovler, <a href="/A047393/b047393.txt">Table of n, a(n) for n = 1..10000</a>
%H A047393 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047393 a(n) = 8*n - a(n-1) - 15 for n>1, a(1)=0. - _Vincenzo Librandi_, Aug 05 2010
%F A047393 From _R. J. Mathar_, Oct 08 2011: (Start)
%F A047393 a(n) = 4*n - 11/2 - 3*(-1)^n/2.
%F A047393 G.f.: x^2*(1+7*x) / ( (1+x)*(x-1)^2 ). (End)
%F A047393 a(n+1) = Sum_{k>=0} A030308(n,k)*A146541(k). - _Philippe Deléham_, Oct 17 2011
%F A047393 Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)+1)*Pi/16 + log(2)/2 + sqrt(2)*log(sqrt(2)+1)/8. - _Amiram Eldar_, Dec 18 2021
%F A047393 E.g.f.: ((8*x - 3)*exp(x) + 3*exp(-x))/2 = 4*x*exp(x) - 3*sinh(x). - _David Lovler_, Aug 02 2022
%p A047393 a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+8 od: seq(a[n], n=0..58); # _Zerinvary Lajos_, Mar 16 2008
%t A047393 Riffle[#, # + 1] & [Range[0, 400, 8]] (* _Paolo Xausa_, Mar 11 2025 *)
%o A047393 (PARI) forstep(n=0,200,[1,7],print1(n", ")) \\ _Charles R Greathouse IV_, Oct 17 2011
%o A047393 (PARI) a(n) = 4*n - 11/2 - 3*(-1)^n/2; \\ _David Lovler_, Jul 25 2022
%o A047393 (Python)
%o A047393 def A047393(n): return n-1<<2 if n&1 else (n<<2)-7 # _Chai Wah Wu_, Mar 11 2025
%Y A047393 Union of A008590 and A017077.
%K A047393 nonn,easy
%O A047393 1,3
%A A047393 _N. J. A. Sloane_
%E A047393 More terms from _James Sellers_, Jun 20 2000