cp's OEIS Frontend

A047452 Numbers that are congruent to {1, 6} mod 8.

%I A047452 #55 Mar 30 2024 01:38:57
%S A047452 1,6,9,14,17,22,25,30,33,38,41,46,49,54,57,62,65,70,73,78,81,86,89,94,
%T A047452 97,102,105,110,113,118,121,126,129,134,137,142,145,150,153,158,161,
%U A047452 166,169,174,177,182,185,190
%N A047452 Numbers that are congruent to {1, 6} mod 8.
%C A047452 Except for 1, numbers whose binary reflected Gray code (A014550) ends with 01. - _Amiram Eldar_, May 17 2021
%H A047452 Muniru A Asiru, <a href="/A047452/b047452.txt">Table of n, a(n) for n = 1..5000</a>
%H A047452 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047452 G.f.: x*(1+5*x+2*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011
%F A047452 E.g.f.: (4 + exp(-x) + (8*x - 5)*exp(x))/2. - _Ilya Gutkovskiy_, May 25 2016
%F A047452 a(n) = A047615(n) + 1. - _Franck Maminirina Ramaharo_, Jul 23 2018
%F A047452 Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+2)*Pi/16 + log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - _Amiram Eldar_, Dec 11 2021
%p A047452 seq(coeff(series(factorial(n)*((4+exp(-x)+(8*x-5)*exp(x))/2), x,n+1),x,n),n=1..60); # _Muniru A Asiru_, Jul 24 2018
%t A047452 Table[(8 n - 5 + (-1)^n)/2, {n, 1, 100}] (* _Franck Maminirina Ramaharo_, Jul 23 2018 *)
%t A047452 CoefficientList[ Series[(2x^2 + 5x + 1)/((x - 1)^2 (x + 1)), {x, 0, 50}], x] (* or *)
%t A047452 LinearRecurrence[{1, 1, -1}, {1, 6, 9}, 51] (* _Robert G. Wilson v_, Jul 24 2018 *)
%o A047452 (Maxima) makelist((8*n - 5 + (-1)^n)/2, n, 1, 100); /* _Franck Maminirina Ramaharo_, Jul 23 2018 */
%o A047452 (GAP) Filtered([0..250], n->n mod 8=1 or n mod 8=6); # _Muniru A Asiru_, Jul 24 2018
%o A047452 (Python)
%o A047452 def A047452(n): return (n<<2)-2-(n&1) # _Chai Wah Wu_, Mar 30 2024
%Y A047452 Cf. A014550, A047398, A047461, A047470, A047524, A047535, A047615, A047617.
%K A047452 nonn,easy
%O A047452 1,2
%A A047452 _N. J. A. Sloane_