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A090570 Numbers that are congruent to {0, 1} mod 9.

%I A090570 #40 Sep 04 2022 12:32:22
%S A090570 0,1,9,10,18,19,27,28,36,37,45,46,54,55,63,64,72,73,81,82,90,91,99,
%T A090570 100,108,109,117,118,126,127,135,136,144,145,153,154,162,163,171,172,
%U A090570 180,181,189,190,198,199,207,208,216,217,225,226
%N A090570 Numbers that are congruent to {0, 1} mod 9.
%H A090570 David Lovler, <a href="/A090570/b090570.txt">Table of n, a(n) for n = 1..1000</a>
%H A090570 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A090570 A145389(a(n)) = A010888(a(n)). - _Reinhard Zumkeller_, Oct 10 2008
%F A090570 a(n) = 9*n - a(n-1) - 17 (with a(1)=0). - _Vincenzo Librandi_, Nov 16 2010
%F A090570 From _R. J. Mathar_, Oct 08 2011: (Start)
%F A090570 a(n) = 9*n/2 - 25/4 - 7*(-1)^n/4.
%F A090570 G.f.: x^2*(1+8*x)/( (1+x)*(1-x)^2 ). (End)
%F A090570 a(n+1) = Sum_{k>=0} A030308(n,k)*A005010(k-1), with A005010(-1)=1. - _Philippe Deléham_, Oct 17 2011.
%F A090570 E.g.f.: 8 + ((18*x - 25)*exp(x) - 7*exp(-x))/4. - _David Lovler_, Sep 03 2022
%e A090570 13 is 1101 in base 2, so a(13+1) = a(14) = 36*1 + 18*1 + 9*0 + 1*1 = 36+18+1 = 55. - _Philippe Deléham_, Oct 17 2011
%o A090570 (PARI) forstep(n=0,200,[1,8],print1(n", ")) \\ _Charles R Greathouse IV_, Oct 17 2011
%Y A090570 Union of A008591 and A017173. - _Reinhard Zumkeller_, Oct 10 2008
%Y A090570 Cf. A010888, A145389.
%Y A090570 Cf. A005010, A030308.
%K A090570 nonn,easy
%O A090570 1,3
%A A090570 _Giovanni Teofilatto_, Feb 25 2004